How did Chazal "know" that Bilaam committed bestiality with his donkey?

How did Chazal "know" that Bilaam committed bestiality with his donkey?

They didn't, but it is a matter of textual interpretation. As mentioned in Avodah Zarah 4b, the words

ההסכן הסכנתי

find a secondary meaning, a double-entendre if you will, of 'warming' by night. They point to the parallel by Avishag haShunamit (though there the warming was non-sexual). As Rashi explains (Bemidbar 22:30):

The she-donkey said to Balaam, "Am I not your she-donkey on which you have ridden since you first started until now? Have I been accustomed to do this to you?" He said, "No."		לוַתֹּ֨אמֶר הָֽאָת֜וֹן אֶל־בִּלְעָ֗ם הֲלוֹא֩ אָֽנֹכִ֨י אֲתֹֽנְךָ֜ אֲשֶׁר־רָכַ֣בְתָּ עָלַ֗י מֵעֽוֹדְךָ֙ עַד־הַיּ֣וֹם הַזֶּ֔ה הַֽהַסְכֵּ֣ן הִסְכַּ֔נְתִּי לַֽעֲשׂ֥וֹת לְךָ֖ כֹּ֑ה וַיֹּ֖אמֶר לֹֽא:
Have I become accustomed: Heb. הַהַסְכֵּן הִסְכַּנְתִּי. As the Targum [Onkelos] renders [lit., have I learned to do this?]. Similarly,“Does man learn (יִסְכָּן) for God?” (Job 22:2). Our Rabbis, however, expounded this verse in the Talmud: They [the Moabite dignitaries] said to him, “Why aren’t you riding on a horse?” He [Balaam] said to them, “I sent it out to pasture.” [Immediately, the she-donkey retorted, “Am I not your she-donkey?” He said to her, “Just for bearing burdens.” She retorted, “on which you have ridden.” He said to her, “Only on occasion.” She retorted,“since you first started until now, and not only that but I provide you with riding by day, and with intimacy at night, (interpreting Heb. הַהַסְכֵּן הִסְכַּנְתִּי as”I heated you up,") as is stated in Tractate Avodah Zarah [4b].		ההסכן הסכנתי: כתרגומו, וכן (איוב כב, ב) הלאל יסכן גבר. ורבותינו דרשו מקרא זה בגמרא אמרו ליה, מאי טעמא לא רכבת אסוסיא. אמר להון ברטיבא שדאי ליה וכו', כדאיתא במסכת עבודה זרה (ד ב):

It seems possible that they also saw a double-entendre in אֲשֶׁר־רָכַ֣בְתָּ עָלַ֗י. That explains the immediate mechanics. What about the impetus?

I can see three impetiuses.

(A) a global desire to paint bad guys negatively
(B) a local desire to expand upon, and explain, the "embarrassment" of the previous verse, in such manner as to make each subsequent phrase an explanation of the "embarrassment", in increasing order.
(C) that the donkey was executed by the angel, as detailed in another midrash; this execution was for sparing of embarrassment, and Chazal found the other instance of execution of an animal to spare embarrassment.

(A) The global desire to paint bad guys negatively

It is a general trend in midrash to take "bad-guy" Biblical characters who are, on a peshat level, painted in shades of gray, and to paint them as totally dark. We see this for Lavan, for Lot, for Esav, for Pharaoh, and so on.

Similarly, for the heroes and "good guys", even where they act in ways which seem not-so-good, the midrash will paint them and their actions as more clearly defined white-hats. And neutral statements on a peshat level will be certainly taken as accounts of praiseworthy actions.

There may be many reasons for this. (Maharatz Chajes discusses this phenomenon at length, IIRC in Iggeret Bikkoret). The purpose of these midrashim may be homiletical, to provide positive role models and vice versa, a Goofus and Gallant. It could be that Chazal are just always going to pick up on this nuanced language, and will naturally and honestly assume that these will be holding hidden condemnation or tales of good deeds. Context dictates which one, and the overall character of the person is the best context.


(B) a local desire to expand upon the "Embarrassment"

The previous verse (22:29, and Rashi) read:

Balaam said to the she-donkey, "For you have humiliated me; if I had a sword in my hand, I would kill you right now."		כטוַיֹּ֤אמֶר בִּלְעָם֙ לָֽאָת֔וֹן כִּ֥י הִתְעַלַּ֖לְתְּ בִּ֑י ל֤וּ יֶשׁ־חֶ֨רֶב֙ בְּיָדִ֔י כִּ֥י עַתָּ֖ה הֲרַגְתִּֽיךְ:
you have humiliated: Heb. הִתְעַלַּלְתָּ. As the Targum [Onkelos] renders it, a term denoting shame and disgrace.		התעללת: כתרגומו לשון גנאי ובזיון:
If I had a sword in my hand: This matter made him greatly contemptible in the eyes of the dignitaries. This man was going to kill an entire nation with his mouth, yet for this she-donkey he needed weapons!- [Mid. Tanchuma Balak 9, Num. Rabbah 20:14]		לו יש חרב בידי: גנות גדולה היה לו דבר זה בעיני השרים, זה הולך להרוג אומה שלמה בפיו, ולאתון זו צריך לכלי זיין:

The word hitalalta is ambiguous, but is understood by Chazal to denote embarrassment, shame, and disgrace. We have an immediate disgrace in the very verse, namely that he did not have the ability to slay the donkey with his own mouth, but would require a weapon.

But the embarrassment and shame, on a peshat level, is that his donkey repeatedly has disregarded his directions! He cannot control his donkey, and so has smote her three times.

But then the embarrassment continues. And the donkey's conversation repeatedly exposes the lowly stature of Bilaam before the Moabite dignitaries, culminating with revelations that he regularly engaged in intimacy with his donkey.

(C) That the donkey was executed by the angel

However, I think a real key to this interpretation is to be found later in the same perek. In pasuk 33:

When the she-donkey saw me, it turned aside these three times. Had she not turned aside before me, now also I would also have killed you and spared her [the she-donkey]."

לגוַתִּרְאַ֨נִי֙ הָֽאָת֔וֹן וַתֵּ֣ט לְפָנַ֔י זֶ֖ה שָׁל֣שׁ רְגָלִ֑ים אוּלַי֙ נָֽטְתָ֣ה מִפָּנַ֔י כִּ֥י עַתָּ֛ה גַּם־אֹֽתְכָ֥ה הָרַ֖גְתִּי וְאוֹתָ֥הּ הֶֽחֱיֵֽיתִי:

and spared her: But now, since she spoke and rebuked you, and you could not withstand her rebuke, as it is written, “He said, No,” therefore, I have killed her, so that [people] should not say, “This is the one that silenced Balaam with her rebuke, and he could not respond,” for the Omnipresent shows regard for human dignity. Similarly, “you shall kill the woman and the animal [through which the sin was committed]” (Lev. 20:16), and, “you shall kill the animal” (ibid. 20:15) - [Mid. Tanchuma Balak 9, Num. Rabbah 20:14]

ואותה החייתי: ועתה מפני שדברה והוכיחתך ולא יכולת לעמוד בתוכחתה, כמו שכתוב (פסוק ל) ויאמר לא. על כן הרגתיה, שלא יאמרו זו היא שסלקה את בלעם בתוכחתה ולא יכול להשיב, שחס המקום על כבוד הבריות, וכן (ויקרא כ, טו - טז) ואת הבהמה תהרוגו, וכן (שם) והרגת את האשה ואת הבהמה:

The clear meaning of this midrash is that it is the embarrassment of rebuke for which the donkey here is killed.

However, Vayikra is one of two times an animal is executed. An animal who kills a person is executed, and there are even full court procedures for it, but the reason seems to be that spelled out in Bereishit 9:5, וְאַךְ אֶת-דִּמְכֶם לְנַפְשֹׁתֵיכֶם אֶדְרֹשׁ, מִיַּד כָּל-חַיָּה אֶדְרְשֶׁנּוּ; וּמִיַּד הָאָדָם, מִיַּד אִישׁ אָחִיו--אֶדְרֹשׁ, אֶת-נֶפֶשׁ הָאָדָם.

The other time is the case of bestiality. Now animals are not typically deemed guilty of sin. Why should the animal be executed for sleeping with a human? This is what the midrash (above) is saying, that it is to spare the human embarrassment and preserve their dignity. The animal cannot be walking around and have people point to it and say it was Ploni's girlfriend or Plonit's boyfriend.

Once this connection had been made, it was a very short leap to say that Bilaam's female donkey was executed to spare him for embarrassment in the exactly the same way the other animal in the Torah was executed to spare someone from embarrassment. And this then guided Chazal in all the other interpretations.

a

Bilaam's true identity

Over Shabbos, I had a revelation about Bilaam:

a) He only had one eye. (Sanhedrin 105a, based on Bemidbar 24:3)
b) While not wanting to live a Jewish life, he wanted to die among the righteous Jews, and so could be considered quasi-Jewish. (Bemidbar 23:20) (Alternatively, ketoafot re'em lo, "he has the horn of the unicorn", in Bemidbar 23:22)
c) He could fly. (Midrash Rabba on Balak)
d) He was royalty - as Bela ben Beor, he was one of the kings of Edom. (Bereishit 36:32)
e) His name is a contraction of bala' 'am, swallower of a people.

Thus:

♫ He was a (a) one eyed, (b) one horned, (c) flying (d) purple (e) people eater. ♪

Balak: Bilaam's transition from sorcerer to prophet

Alternate Title: Hashem is consistent

A sorcerer manipulates spiritual forces, and thinks he can manipulate God as just another spiritual force. A prophet is the mouthpiece of God and the conduit of his will.

A surface reading of parshat Balak is confusing. Hashem seems inconsistent. Hashem tells Bilaam not to go. Then, He tells him that he may go. Then, Hashem sends an angel to stop (or kill) Bilaam for going. Then, the angel tells him that he may go? Is this not an inconsistency or repeated reversal? It all seems quite confusing.

The answer, to my mind, is that Hashem is entirely consistent, but what we are seeing is character development. The messengers ask Bilaam (22:6) to curse them, for they know that whoever he curses is cursed. That is, he has the role of sorcerer, able to manipulate spiritual forces.

Bilaam tells them he will sleep and ask Hashem. Hashem has at least some role in this. Hashem tells him not to go, and furthermore, that he shouldn't curse them, for they are blessed. And, as Bilaam relates to the messengers, Hashem refused to let him go with them (22:13).

This initial refusal establishes two things. First, it clearly reveals Hashem's desire to Bilaam. Hashem does not want Bilaam to go, and doesn't want Bilaam to curse. Any action / intention by Bilaam to curse them would violate what Hashem wants, and is therefore at least quasi-sinful. Furthermore, it is likely a theological rejection of (2:6), that the power to curse lies entirely in Bilaam's hand. Rather, this people is objectively blessed, and so a curse should not / will not happen.

Bilaam tells the messengers this. Other messengers from Balak come and repeat the request. He seems pious and says to them he cannot act except as Hashem instructs, and acts as a conduit to relate Hashem's request.

However, the subtext here is that he does indeed wish to go, given that Balak has promised honor and riches. Yet Bilaam already knows the will of Hashem. Hashem's prior response made it absolutel clear that Hashem did not wish Bilaam to curse them, and that they are blessed, such that he should not curse. Bilaam should have simply held to the prior rejection.

That he does not shows that (1) he is hoping for permission to act in a way which will bring him honor and riches, even though he knows that this is contrary to Hashem's desires, and (2) he still thinks that there is power in his words, and that he will be able to manipulate spiritual forces to curse those who are blessed.

Hashem tells him to go with the men, but that he will do that which Hashem tells him, he should do. While on a surface level, this seems like clear authorization to go. But it is really a passive-aggressive answer. It is also a test. Will Bilaam go, now that he has official permission? He already knows that going and cursing is against Hashem's desire. And Bilaam still thinks that he will somehow succeed in eventually cursing. He is acting as sorcerer.

When Bilaam goes, Hashem's wrath flares (22:22). This is not inconsistent. The angel is not, however, sent to kill, but to deliver a message. The donkey, three times, sees an angel standing in his path, and veers to the side. The dumb donkey understands Hashem's will (represented by the angel), and diverts from his intended action, and direction from his human master, in order to fulfill Hashem's will. So too, Bilaam should have understood (from his first interaction with Hashem; perhaps also from the repeated strange veering to the side by his donkey) that this mission is contrary to Hashem's true desire, and should have diverted from his intended action, and direction from his human master Balak, in order to fulfill Hashem's will.

His own words rebuking the donkey, first beating it, and saying it was deserving of death for going against his will, such that if he had a sword, he would kill it, is a condemnation of himself, who went against his own Master's desire. He then sees the angel, with a sword parallel to the sword he just mentioned.

When the donkey speaks, and Bilaam sees the angel with sword drawn, Bilaam understands that Hashem is upset with him, for his attitude and sin - for his wanting to accomplish something he knew was contrary to Hashem's desire, and for his belief that he would somehow be able to manipulate the spiritual forces contrary to how Hashem was running the world.

Bilaam states his willingness to return, since this has displeased Hashem (22:34). This is a (partial, at least) transformation, in that he will only act in accordance with Hashem's pleasure or displeasure. Hashem tells Bilaam to go, but that he will speak only what Hashem instructs him (22:35).

At this point, Bilaam is no longer sinning. It is Hashem's will that he go. Hashem's intention here is to make public, to the nation of Moav, that Hashem is in control of the course of human events, and of who is cursed or blessed. Bilaam is playing the role of the donkey. Just as the Hashem opened the donkey's mouth and it said the words Hashem placed in its mouth, so too Bilaam. And the three times diversion from human master's direction because of Hashem's direction will parallel the three times Bilaam will veer from Balak's direction.

When greeting Balak, he doesn't say that he can only act as Hashem wants him to act, which is the earlier pious statement. He declares that he has no power to say anything (22:38). This is contrary to what the messengers first said (22:6), that the power to curse was with Bilaam. He further tells Balak (22:38) that he is a mere mouthpiece, and only says that which Hashem puts into his mouth. This is new. This is the lesson he learned on the road, from the donkey and the angel. This is what Hashem said in 22:35, that he will (not just should) speak only that which Hashem gives him to speak.

Balak still operates on the assumption that Bilaam will be able to curse - will be able to channel and manipulate spiritual forces, via kesamim (which were in the hands of the messengers). The sacrifices are initiated, at first, by Balak (22:40), unless this is part of simply honoring Bilaam.

At any rate, sacrifices (and IIRC, drinking the blood of sacrifices) are a mantic method, a means of inducing a prophetic altered state. Thus, seven altars with seven bulls and seven rams, and the hope that Hashem will appear to Bilaam, this time in the daytime rather than in a dream. This is ritualistic, and means of manipulating spiritual forces. Yet Bilaam states that Hashem will show him something that he can tell Balak (23:3).

Now, he acts as prophet, rather than sorcerer. He rejects, to Bilaam, to Moav, to the reader of the sidra, the idea that he will have any power to curse or invoke wrath if this is not Hashem's desire in the world (23:8). And then proceeds to bless Israel.

Balak is upset with Bilaam, because he does not regard Bilaam as prophetic conduit, but someone who can control spiritual forces, so Bilaam tells him otherwise, that he must say that which Hashem puts in his mouth (23:12). Balak persists, the scene repeats, with similar result, with the same idea that it is Hashem who puts the words in his mouth (23:26), such that even positive words he will not / cannot suppress. Balak still thinks Hashem is manipulable, such that a different location and further sacrifices will induce Hashem to act in contrary manner to His expressed desire (23:27).

Then, there is a further positive development in Bilaam's attitude. He sees what Hashem's desire is, and doesn't go through any or his sorcerer actions. He sees Hashem's will to bless Israel, and doesn't go in search of omens as before, in a feeble / fake / ultimately ineffective way to attempt to manipulate the result (24:1). And then speaks poetically and prophetically, blessing the nation of Israel. This might even be of Bilaam's own accord and invention!

Contrary to all I have written is perhaps Bilaam's claim (24:12) that this is the original statement to the second messengers (22:18). But this might well be cast as spin, and we can see a slight difference in language (acting contrary to His will, which is the piety of a sorcerer vs. ability to effect anything with speech, since Hashem is giving him the words, which is the capability of a prophet). 

Derech eretz for Avraham and Bilaam

In Taama deKra on Vayera, Rav Chaim Kanievsky points out an interesting discrepancy between Rashi on Vayera and Rashi on Balak:

That is, the pasuk and Rashi in Vayera (Bereishit 22:3) read:

And Abraham arose early in the morning, and he saddled his donkey, and he took his two young men with him and Isaac his son; and he split wood for a burnt offering, and he arose and went to the place of which God had told him.

ג. וַיַּשְׁכֵּם אַבְרָהָם בַּבֹּקֶר וַיַּחֲבשׁ אֶת חֲמֹרוֹ וַיִּקַּח אֶת שְׁנֵי נְעָרָיו אִתּוֹ וְאֵת יִצְחָק בְּנוֹ וַיְבַקַּע עֲצֵי עֹלָה וַיָּקָם וַיֵּלֶךְ אֶל הַמָּקוֹם אֲשֶׁר אָמַר לוֹ הָאֱלֹהִים:

his two young men: Ishmael and Eliezer, for a person of esteem is not permitted to go out on the road without two men, so that if one must ease himself and move to a distance, the second one will remain with him. — [from Pirkei d’Rabbi Eliezer, ch. 31; Gen. Rabbah ad loc., Tan. Balak 8]

את שני נעריו: ישמעאל ואליעזר, שאין אדם חשוב רשאי לצאת לדרך בלא שני אנשים, שאם יצטרך האחד לנקביו ויתרחק יהיה השני עמו:

while the pasuk and Rashi in Balak (Bemidbar 22:22) read:

God's wrath flared because he was going, and an angel of the Lord stationed himself on the road to thwart him, and he was riding on his she-donkey, and his two servants were with him.

כב. וַיִּחַר אַף אֱלֹהִים כִּי הוֹלֵךְ הוּא וַיִּתְיַצֵּב מַלְאַךְ יְהֹוָה בַּדֶּרֶךְ לְשָׂטָן לוֹ וְהוּא רֹכֵב עַל אֲתֹנוֹ וּשְׁנֵי נְעָרָיו עִמּוֹ:

and his two servants were with him: From here we learn that a distinguished person who embarks on a journey should take two people with him to attend him, and then they can attend each other [so that when one is occupied, the other takes his place]. — [Mid. Tanchuma Balak 8, Num. Rabbah 20:13]

ושני נעריו עמו: מכאן לאדם חשוב היוצא לדרך יוליך עמו שני אנשים לשמשו וחוזרים ומשמשים זה את זה:

In both cases, Rashi states that this is derech eretz to have two men to attend him. However, in Vayera, Rashi states explicitly that it so that if one attendant needs to defecate, which requires moving to a distance, the other can remain with him. Meanwhile, in Balak, Rashi appears to say that besides attending him, they are attending each other. [The bracketed text in English in the second Rashi is an attempted harmonization, rather than something explicit in Rashi.] This seems to indeed be a discrepancy.

Rav Chaim Kanievsky offers a rather clever resolution. He points to Sanhedrin 104b [the citation in the text which has 105b is in error] which states:

Our Rabbis taught: It once happened that two men [Jews] were taken captive on Mount Carmel, and their captor was walking behind them. One of them said to the other, 'The camel walking in front of us is blind in one eye, and is laden with two barrels, one of wine, and the other of oil, and of the two men leading it, one is a Jew, and the other a heathen.' Their captor said to them, 'Ye stiff-necked people, whence do ye know this?' They replied, 'Because the camel is eating of the herbs before it only on the side where it can see, but not on the other, where it cannot see.¹  It is laden with two barrels, one of wine and the other of oil: because wine drips and is absorbed [into the earth], whilst oil drips and rests²  [on the surface].³  And of the two men leading it, one is a Jew, and the other a heathen: because a heathen obeys the call of Nature in the roadway, whilst a Jew turns aside.' He hastened after them, and found that it was as they had said.⁴  So he went and kissed them on the head,⁵  brought them into his house, and prepared a great feast for them. He danced [with joy] before them and exclaimed 'Blessed be He who made choice of Abraham's seed and imparted to them of His wisdom, and wherever they go they become princes to their masters!' Then he liberated them, and they went home in peace.

The relevant portion of this tale is that the captive Jews reasoned that ahead of them on the road was one Jew and one gentile, 'because a heathen obeys the call of Nature in the roadway, whilst a Jew turns aside'. If so, for Avraham and his servants, the explanation of turning aside works. Meanwhile, from Bilaam and his servants, the explanation of turning aside does not work.

This is a rather neat resolution. I suspect that, besides a bekius in Shas, the connection was aided by the proximity of Sanhedrin 104b, with this tale, to Sanhedrin 105a, which discusses midrashim about Bilaam, in reference to the events of parashat Balak.

Still, I don't think that this resolution is correct. Here are a few objections:

_____

1) Avraham went with Eliezer and Yishmael, and Bilaam went with two servants. The ones who would distance themselves in this scenario would be Eliezer, Yishmael and [not] the two servants. If so, the contrast is not between Avraham and Bilaam, but of their attendants. Still, this particular objection can be readily dismissed. Eliezer (as an eved kenaani) and Yishmael (as son of Avraham) would be expected to conduct themselves appropriately, distancing themselves when relieving themselves.

2) More to the point, when these Rashis speak of derech eretz for an adam chashuv, the idea is that this is conduct with dignity. Both Avraham and Bilaam momentarily abandoned that dignity, Avraham for zerizut for the mitzvah and Bilaam for hatred (see the Rashis in proximity). Yet here, in taking two attendants, they are conducting themselves with dignity.

When the gemara in Sanhedrin speaks, in the tale, of the difference between Jews and heathens, in that Jews will turn aside while the heathens will defecate in the middle of the road, the point of distinction is that the Jews are conducting themselves with dignity. Bilaam, conducting himself as an adam chashuv, would not defecate in the middle of the road. What of the attendants? Do you really think it dignified for Bilaam to be attended upon by a servant while the servant defecates next to him on the road?

3) The wording of Rashi (drawn from Midrash Tanchuma) is מכאן לאדם חשוב היוצא לדרך יוליך עמו שני אנשים לשמשו וחוזרים ומשמשים זה את זה. That is, we, who are Jewish people, are supposed to derive a lesson of proper conduct for a Jewish adam chashuv from this. Would the midrash really, then, substitute a weaker reason (of them attending one another) which only is relevant to non-Jews?

____

Some commentators note this discrepancy in Rashi and attempt to harmonize. For instance, see Siftei Chachamim on the Rashi in Balak, where the "attending on one another" is that one does the attending that the other would do, when one of them excuses himself to use the bathroom.

Etz Yosef on the Midrash Tanchuma in Balak says likewise. This is a plausible harmonization, though one needs to force it into the words a bit. The simpler meaning is that the attendants attend one another. The man is so chashuv that even his attendants have attendants!

I would rather not focus (for now at least) on the meaning of these two statements. Maybe one should harmonize, and Tanchuma means the same as what Rashi said in Vayera, and maybe one should not harmonize.

However, I would guess that the reason for the difference in Rashi stems from a difference in wording from Rashi's sources. That is, Rashi does not typically make things up, based on sevara, but rather channels midrashim. We saw Rashi's sources cited above. Let us repeat them. In Vayera:

And Abraham arose early in the morning, and he saddled his donkey, and he took his two young men with him and Isaac his son; and he split wood for a burnt offering, and he arose and went to the place of which God had told him.

ג. וַיַּשְׁכֵּם אַבְרָהָם בַּבֹּקֶר וַיַּחֲבשׁ אֶת חֲמֹרוֹ וַיִּקַּח אֶת שְׁנֵי נְעָרָיו אִתּוֹ וְאֵת יִצְחָק בְּנוֹ וַיְבַקַּע עֲצֵי עֹלָה וַיָּקָם וַיֵּלֶךְ אֶל הַמָּקוֹם אֲשֶׁר אָמַר לוֹ הָאֱלֹהִים:

his two young men: Ishmael and Eliezer, for a person of esteem is not permitted to go out on the road without two men, so that if one must ease himself and move to a distance, the second one will remain with him. — [from Pirkei d’Rabbi Eliezer, ch. 31; Gen. Rabbah ad loc., Tan. Balak 8]

את שני נעריו: ישמעאל ואליעזר, שאין אדם חשוב רשאי לצאת לדרך בלא שני אנשים, שאם יצטרך האחד לנקביו ויתרחק יהיה השני עמו:

I've looked at Pirkei deRabbi Eliezer, perek 31, and saw no reference to adam chashuv. I think they are simply sourcing the identification of these two young men as Yishmael and Eliezer. This identification indeed appears in Pirkei deRabbi Eliezer. See line 23-24:

Bereishit Rabba 55:7 has this source for Rashi:

ויקח את שני נעריו אתו. 
אמר רבי אבהו:שני בני אדם נהגו בדרך ארץ: אברהם ושאול. 
אברהם, שנאמר: ויקח את שני נעריו. 
שאול, (ש"א כ"ח) וילך הוא ושני אנשים עמו. 

"And he took his two young men with him. Rabbi Abahu said: two people conducted themselves with derech eretz, namely Avraham and Shaul. Avraham, as it is said 'And he took his two young men with him'. Shaul, (I Shmuel 28) 'And he went, and two men with him'."

Note that Rabbi Abahu here does not reckon Bilaam as one who conducted himself with derech eretz. Bilaam is not on the radar.

Neither of these two sources speak specifically about the reason for two attendants. Perhaps Rashi supplemented this himself. Perhaps he looked to the distance, and was indeed interpreting Tanchuma on Balak. I still would not leap to say that he drew this from Balak. Perhaps there is still some other midrashic source which states this explicitly.

The pasuk and Rashi in Balak were:

God's wrath flared because he was going, and an angel of the Lord stationed himself on the road to thwart him, and he was riding on his she-donkey, and his two servants were with him.

כב. וַיִּחַר אַף אֱלֹהִים כִּי הוֹלֵךְ הוּא וַיִּתְיַצֵּב מַלְאַךְ יְהֹוָה בַּדֶּרֶךְ לְשָׂטָן לוֹ וְהוּא רֹכֵב עַל אֲתֹנוֹ וּשְׁנֵי נְעָרָיו עִמּוֹ:

and his two servants were with him: From here we learn that a distinguished person who embarks on a journey should take two people with him to attend him, and then they can attend each other [so that when one is occupied, the other takes his place]. — [Mid. Tanchuma Balak 8, Num. Rabbah 20:13]

ושני נעריו עמו: מכאן לאדם חשוב היוצא לדרך יוליך עמו שני אנשים לשמשו וחוזרים ומשמשים זה את זה:

We can safely ignore Bamidbar Rabba, which is likely post-Rashi and does not serve as Rashi's source (and which says the same as Tanchuma anyway). Rashi got this from Tanchuma Balak, which states:

ושני נעריו עמו זה דרך ארץ, אדם חשוב היוצא לדרך, צריך שנים לשמשו, וחוזרין ומשמשין זה לזה. 

Note that Tanchuma on parashat Vayera takes no note of Avraham taking along two attendants.

The picture I am trying to draw here is of two midrashim which operate in parallel, which do not know of each other. Rabbi Abahu in Bereishit Rabba only knows of Avraham and Shaul and does not know of Bilaam. Midrash Tanchuma only knows of Bilaam and does not know of Bilaam. If so, the reasoning within these two midrashic traditions also do not need to match. (To return to the topic of whether one should harmonize, this might help strip our impetus to harmonize the Rashis.)

And don't complain to Rashi about discrepancies. Rashi in Balak did not say the explanation of an attendant distancing himself to defecate because he was citing Midrash Tanchuma verbatim. He would not have changed the midrash without cause. Perhaps one could complain to Rashi about his explanation in Vayera, but then, we don't necessarily have Rashi's source.

A house full of wealth

Consider the following pasuk and Rashi in Balak:

Balaam answered and said to Balak's servants, "Even if Balak gives me a house full of silver and gold, I cannot do anything small or great that would transgress the word of the Lord, my God.		יח. וַיַּעַן בִּלְעָם וַיֹּאמֶר אֶל עַבְדֵי בָלָק אִם יִתֶּן לִי בָלָק מְלֹא בֵיתוֹ כֶּסֶף וְזָהָב לֹא אוּכַל לַעֲבֹר אֶת פִּי יְהֹוָה אֱלֹהָי לַעֲשׂוֹת קְטַנָּה אוֹ גְדוֹלָה:
a house full of silver and gold: This shows us that he was greedy and coveted other people’s money. He said, “He ought to give me all his silver and gold, since he has to hire many armies, and even then, it is questionable whether he will be victorious or not, whereas I will certainly succeed.”- [Mid. Tanchuma Balak; Num. Rabbah 20:10]		מלא ביתו כסף וזהב: למדנו שנפשו רחבה ומחמד ממון אחרים. אמר, ראוי לו ליתן לי כל כסף וזהב שלו, שהרי צריך לשכור חיילות רבות, ספק נוצח ספק אינו נוצח, ואני ודאי נוצח:

I found the following summary of a Torah Temima in Prachei Rashi:

Torah Temimah:

After citing the Rashi, Torah Temimah writes:

"And there is to comment on this. For do we not find in Pirkei Avot 9:6: 'Rabbi Yossi ben Kisma said: If you were to give me all the silver and gold in the world, I would not travel to a place which was not a place of Torah..." And if so, why do we see fit to darshen this one [by Bilaam] negatively, in such language as to the disgrace of Bilaam? 

However, the truth is that this case is not comparable to that one there. For there [in Avot] the story was that a certain person suggested before Rabbi Yossi that he travel to dwell in his city, and that he would give him for this a million gold dinarii, and upon this Rabbi Yossi responded the aforementioned response. And therefore, Rabbi Yossi was compelled to respond to him in similar fashion to the suggestion, that not only would he not take a million gold dinarii, but even all the silver and gold in the world. In contrast here, Balak did not suggest to Bilaam that he would enrich him with silver because of his action, but only promised him that he would honor him, as it states (pasuk 17) 'for I will surely honor you'. 

And if so, Bilaam should have replied in like fashion to his suggestion, that he could not be honored in any honor if it entailed transgressing the word of Hashem. So why did he respond in matters of money? Rather, certainly because he was desirous of money. And this is as is known in nature, that a person's desire is always on his tongue to mention it.'

End quote. The Mishna in Avot reads:

פעם אחת הייתי מהלך בדרך ופגע בי אדם אחד ואמר לי שלום, החזרתי לו שלום. אמר לי, רבי מאיזו עיר אתה? אמרתי לו מעיר גדולה של חכמים וסופרים אנוכי. אמר לי רבי רצונך שתדור עמנו במקומנו, ואני אתן לך אלף אלפים כסף וזהב אבנים טובות ומרגליות? אמרתי לו, אם אתה נותן לי כל כסף וזהב אבנים טובות ומרגליות שבעולם, איני דר אלא במקום תורה! שכך כתוב בספר התהילים "טוב לי תורת פיך מאלפי זהב וכסף"

I certainly agree with the distinction that Torah Temimah is making here. Given the offer by the unnamed man, Rabbi Yossi ben Kisma's response is natural in context and does not reflect any flaw in Rabbi Yossi ben Kisma's nature.

I would tentatively express some slight doubt about Bilaam's response being out of context, however. While Torah Temimah's analysis makes good sense and is quite compelling, we should subject it to scrutiny, considering it in the light of the peshat in the pasuk and in light of Rashi's sources. We shall see.

First off, consider that according to Ibn Ezra, Balak's offer was indeed one of money.

 כי כבד אכבדך -בממון.

וכל אשר תאמר -שיש צורך כדי שתקללם, והעד: כי כבד אכבדך כן שאמר בלעם: אם יתן לי בלק מלא ביתו כסף וזהב:

Thus, Ibn Ezra considered "surely honor you" to be ambiguous, and so takes Bilaam's response as clarifying what it was that Balak offered. Perhaps compare with the root יקר which means both heavy and expensive.

Of course, Rashi is not Ibn Ezra, so Rashi does not need to agree that Balak was offering wealth. However, consider this earlier pasuk and Rashi:

He sent messengers to Balaam the son of Beor, to Pethor, which is by the river of the land of his people, to call for him, saying, "A people has come out of Egypt, and behold, they have covered the "eye" of the land, and they are stationed opposite me.

ה. וַיִּשְׁלַח מַלְאָכִים אֶל בִּלְעָם בֶּן בְּעוֹר פְּתוֹרָה אֲשֶׁר עַל הַנָּהָר אֶרֶץ בְּנֵי עַמּוֹ לִקְרֹא לוֹ לֵאמֹר הִנֵּה עַם יָצָא מִמִּצְרַיִם הִנֵּה כִסָּה אֶת עֵין הָאָרֶץ וְהוּא ישֵׁב מִמֻּלִי:

to call for him: This invitation was for him, [i.e.,] for his benefit, for he promised him a large sum of money. - [Mid. Tanchuma Balak 4, Num. Rabbah 20:7]

לקרא לו: הקריאה שלו היתה ולהנאתו, שהיה פוסק לו ממון הרבה:

This shows that money, and not just honor, was on the table.

(Our Tanchuma does not mention money but honor here:

לקרוא לושכתב לו, שלא תהא סבור שלעצמי בלבד אתה עושה ואני מכבדך. 
אם תעקרם, מכל האומות אתה מתכבד, וכנענים ומצרים כלם משתחווים לך. 

Rashi often has a different version of Tanchuma than we have, so we should consider the possibility that he is basing himself on a different version of Tanchuma, rather than changing it.
)

Then, a bit later, in Balak's actual offer:

For I will honor you greatly and do whatever you tell me to do. So please come and curse this people for me.'"		יז. כִּי כַבֵּד אֲכַבֶּדְךָ מְאֹד וְכֹל אֲשֶׁר תֹּאמַר אֵלַי אֶעֱשֶׂה וּלְכָה נָּא קָבָה לִּי אֵת הָעָם הַזֶּה:
For I will honor you greatly: I will give you more than you have ever received in the past. — [Mid. Tanchuma Balak 6, Num. Rabbah 20:10]		כי כבד אכבדך מאד: יותר ממה שהיית נוטל לשעבר אני נותן לך:

What is the thing of which Balak will give him more? This might be money. But on the other hand, given the context in both Rashi and Tanchuma of honor as a thread running through this, and given that the pasuk itself uses the word כַבֵּד, this can indeed mean more honor.

(The Tanchuma from which this is taken:
כי כבד אכבדך מאד יותר ממה שהיית נוטל לשעבר, אני נותן. 

)

So I think Torah Temimah's explanation can indeed work out, with a shift from honor to money, but with the asterisk that, according to Rashi (and perhaps according to Tanchuma), Balak did indeed promise him a lot of money. And it makes good sense that Rabbi Yossi ben Kisma was responding to an immediate offer of a tremendous treasure, which then makes his idiomatic use of "all the money in the world" not reflective of his personality.

I think that there is another potential explanation, besides that of Torah Temimah. Rabbi Yossi ben Kisma was established based on other evidence as a tzaddik. Meanwhile, Bilaam was established based on other evidence as a rasha. One thing that midrash tends to do is take Biblical characters who are "grey" and paint them as either black or white. Esav is ambiguous, and we can almost see his side. Cheated out of his birthright, because he came in from the field starving. However, the midrash piles on three grievous sins that he had just committed. Yaakov lies to his father about his identity. The midrash breaks up his words so that he just says "It is I. Esav is your firstborn." This is perhaps because the words which are often grabbed for midrashic analysis is ambiguous, and so can be interpreted one way or the other. And the cue for the direction of analysis is taken from their overall sense of the person. Alternatively, there is a homiletic purpose behind such analyses.

It is not just this one trait which the Midrash Tanchuma points out. It is one of three:

ויען בלעם ויאמר אל עבדי בלק אם יתן לי בלק מלא ביתו כסף וזהב וגו' מכאן אתה למד, שהיה בו שלשה דברים, אלו הן: 
עין רעה,
ורוח גבוהה,
ונפש רחבה. 
[עין רעה, דכתיב: וישא בלעם את עיניו וירא את ישראל. רוח גבוהה, דכתיב: מאן ה' לתתי להלך עמכם. נפש רחבה, דכתיב: אם יתן לי בלק וגו']. אלו היה מבקש לשכור חיילות להלחם כנגדן, ספק נוצחין, ספק נופלין. לא דיו שיתן כך ונוצח. הא למדת, שכן בקש. לא אוכל לעבור. 
נתנבא שאינו יכול לבטל ברכות שנתברכו האבות מפני השכינה. ועתה שבו נא בזה גם אתם הלילה. 

Why does Rashi bother defining ויגר?

Parashat Balak begins (pesukim and Rashi):

Balak the son of Zippor saw all that Israel had done to the Amorites.		ב. וַיַּרְא בָּלָק בֶּן צִפּוֹר אֵת כָּל אֲשֶׁר עָשָׂה יִשְׂרָאֵל לָאֱמֹרִי:
Balak… saw all that Israel had done to the Amorites: He said, “These two kings whom we relied on could not resist them; we certainly cannot.” Consequently, “Moab became terrified.” - [Mid. Tanchuma Balak 2, Num. Rabbah 20:2]		וירא בלק בן צפור את כל אשר עשה ישראל לאמורי: אמר אלו שני מלכים שהיינו בטוחים עליהם לא עמדו בפניהם, אנו על אחת כמה וכמה. לפיכך ויגר מואב:
3. Moab became terrified of the people, for they were numerous, and Moab became disgusted because of the children of Israel.		ג. וַיָּגָר מוֹאָב מִפְּנֵי הָעָם מְאֹד כִּי רַב הוּא וַיָּקָץ מוֹאָב מִפְּנֵי בְּנֵי יִשְׂרָאֵל:
[Moab] became terrified: [Heb. וַיָּגָר is] a term denoting dread, as in,“Fear (גּוּרוּ) for yourselves” (Job 19:29). - [Machbereth Menachem p. 59, third def.]		ויגר: לשון מורא, כמו (איוב יט, כט) גורו לכם

The following analysis, from R' Ovadia miBartenura, is reprinted in the sefer Prachei Rashi:

That is, he starts with a slightly different citation of Rashi, which stuffs together the first Rashi (אמר אלו שני מלכים) with the beginning of the second (לשון מורא). R' Ovadia miBartenura writes:

"It is difficult, that which Rashi needs to explain from what Balak was afraid, for the pasuk explains the basis for his fear! It is further difficult why he needs to explain that ויגר is a language of fear, for this is obvious! 

And there is to say, and resolve these matters, in the following manner: Since the pasuk did not say 'And Balak the king of Moav saw", we derive that Balak was not primary in this matter. And further, since it is written after that 'And Moav feared", and it is not written 'And Balak feared', the seeing was ascribed to Balak and the fear to Moav.  

Therefore it seems appropriate to explain that Balak himself did not take the choice in this matter, but rather Moav; they were the ones who employed the stratagems. But the seeing was ascribed to Balak to tell you that even Balak ben Tzipor, who was a mighty warrior known for his might, as is written (in Shofetim 11) "are you really better than Balak ben Tzipor?", even he directed his heart to see all that Israel had done to the Emorites, but he did not fear as Moav feared, for he was not yet king over them, as Rashi explains soon (pasuk 4, d"h בעת ההוא). And since Moav saw that even Balak saw and put in his heart to contemplate the matter, they were quite scared and frightened. And this is what Rashi explains, 'therefore, ויגר מואב." That is to say, because of the seeing of Balak, they were afraid. 

And Rashi needed to explain ויגר as a language of fear because I could have explained it as a language of gathering, such as אוגר בקיץ, and like לא תגורו מפני איש, which they darshen as don't enter in your words, and I would have explained that Balak commanded to gather in Moav and to enter them into the fortified cities because of fear of Israel. 

Therefore he explained ויגר as a language of fear, because it is not possible to explain it as gathering, because the word מאד (the adverb 'greatly'), which follows it, does not apply to it: וַיָּגָר מוֹאָב מִפְּנֵי הָעָם מְאֹד. Meanwhile, as a language of fear, the word מאד can apply, that is to say, they feared greatly."

End quote.

This is an interesting and creative explanation, but I believe that it reads way too much into Rashi. If Rashi meant something so elaborate and non-obvious, I would have expected him to say more.

I don't know the answers to these questions, but I can venture a guess or two, based on Rashi's sources. Like a true golem, I will consider the ויגר as fear first.

That pasuk and Rashi again:

Moab became terrified of the people, for they were numerous, and Moab became disgusted because of the children of Israel.		ג. וַיָּגָר מוֹאָב מִפְּנֵי הָעָם מְאֹד כִּי רַב הוּא וַיָּקָץ מוֹאָב מִפְּנֵי בְּנֵי יִשְׂרָאֵל:
[Moab] became terrified: [Heb. וַיָּגָר is] a term denoting dread, as in,“Fear (גּוּרוּ) for yourselves” (Job 19:29). - [Machbereth Menachem p. 59, third def.]		ויגר: לשון מורא, כמו (איוב יט, כט) גורו לכם

So Rashi is citing Menachem ben Saruk. That might be reason enough for this comment, since Rashi often cited Machberet Menachem, and this is citation / channeling of sources rather than necessarily being entirely bothered by something such that Rashi is prompted to comment. We have access to Machberet Menachem, here. The entry starts on page 58 and continues on to page 59, for the root גר, and he gives 11 different definitions of the root. And the third definition reads:

The fourth definition is asifa, gathering, just as Bartenura mentioned. There are other definitions, such as dwelling. Or this one also might be plausible, given the context of Moav: וַיֹּאמֶר ה' אֵלַי 'אֶל תָּצַר אֶת מוֹאָב וְאַל תִּתְגָּר בָּם מִלְחָמָה.

I would guess that because this is a relatively uncommon word, and because there are 11 possible definitions, and because it is the subject of an entry in Menachem ben Saruk's dictionary, Rashi believed that it was appropriate to clarify, and to offer another example, taking from the first words of the dictionary entry. This doesn't mean (contra Bartenura) that Rashi really considered alternatives, such as 'gathering', remotely plausible, if not for the adverb מאד.

Another reason Rashi perhaps saw fit to define ויגר is that the midrash Tanchuma (one of Rashi's primary sources) actually interprets this in several different ways, the last of which is indeed fear. Thus (siman 2):

ויגר מואב 

מהו ויגר? 
כשהיו ישראל נראין לעמונים, נראים עטופים לשלום. 
וכשנראים למואבים, נראים מזויינים למלחמה, שכך כתיב: וקרבת מול בני עמון, אל תצורם (דב' ב יט). 
כתיב: למלחמה, שכך כתיב: וקרבת מול בני עמון, אל תצורם (דב' ב יט) 
כתיב: כל מין צרה אל תצר להם. 

ואל תתגר בם (שם) כל מין גירוי. 
ולמואבים אמר: אל תצר את מואב ואל תתגר בם מלחמה (שם שם ט). 
מלחמה אין אתה עושה, ומה שאתה יכול לחטוף מן החוץ, חטוף. 
ולפיכך נראים מזויינים, והם נאגרין לעריהם, שאין ויגר אלא לשון אסיפה, שנאמר: אוגר בקיץ בן משכיל (משלי י ה).

While referencing וְאַל תִּתְגָּר בָּם מִלְחָמָה, in the end the midrash interprets this as gathering. Despite the word מאד.

And next, meaning to dwell in non-permanent fashion:

דבר אחר: 
ויגר לשון גר, שהיו רואין לעצמן כגרים בעולם. 
ואמרו: ירדו למצרים לגור והאחזו אותה, והיו משכירין להם בתים, שנאמר: ושאלה אשה משכנתה ומגרת ביתה(שמות ג כב). 

And finally, fear:

דבר אחר: 
ויגרלשון יראה, שהיו מתיראין, שראו כל הארץ ביד ישראל, שבא סיחון ונטל ארץ מואב, שנאמר: והוא נלחם במלך מואב הראשון וגו' ( במ' כא כו). 
ועוג נטל את כל ארץ בני עמון, שנאמר: כי רק עוג מלך הבשן נשאר מיתר הרפאים וגו' (דבר' ג יא). 
באו ישראל נטלוה משניהם, גזל שאין בו עולה. 
והיו אלו רואים את ארצם ביד ישראל, והיו אומרים: לא אמר הקדוש ברוך הוא, כי לא אתן לך מארצו ירושה (שם ב ט), והרי ארצנו לפניהם, לכך היו מתיראין. 

If so, Rashi is selecting from amongst the various midrashic interpretations and choosing the one which is peshat.

Turning now to what Balak saw, I don't think that we can sustain R' Ovadia miBartenura's assertion that Balak didn't fear but merely contemplated. After all, Rashi is channeling Tanchuma (and all these also appear in Bemidbar Rabba):

משל למה הדבר דומה? 
למלך שהושיב שומרים לשמרו מן הגייס, והוא בטוח עליהם שהיו גיבורים. עבר הגייס והרגם, והיה מרתת על עצמו. 
ואף כך בלק ראה מה נעשה בסיחון ובעוג שהיה מעלה להם שכר לשמרו והיה מתיירא מעצמו. ועוד שראה נסים שעשה להם הקדוש ברוך הוא בנחלי ארנון. 

The midrash explicitly says that Balak was afraid, והיה מתיירא מעצמו. It is true that both Rashi and midrash Tanchuma mention that Balak was appointed after the killing of Sichon:

at that time: He was not entitled to the monarchy. He was one of the Midianite nobles [according to some: of the nobles of Sihon (Josh. 13:21)], and when Sihon died, they appointed him over them on a temporary basis. — [Mid. Tanchuma Balak 4, Num. Rabbah 20:4]

בעת ההוא: לא היה ראוי למלכות. מנסיכי מדין היה, וכיון שמת סיחון מנוהו עליהם לצורך שעה:

However, he could still be afraid, given his new role as king. And see the previous perek, Bemidbar 21, where the Israelites attack and kill Og after attacking and killing Sichon.

Furthermore, while it might be obvious what Balak was afraid of from the very words of the pasuk, אֵת כָּל אֲשֶׁר עָשָׂה יִשְׂרָאֵל לָאֱמֹרִי, once we realize that Rashi is channeling his sources and selecting what to say, we know that Rashi actually did have a choice and has made a selection here.

Namely, Balak could either have been afraid because of the death of Sichon and Og -- which is personal, and also accords with the simple peshat of the pasuk. Or, he could have been afraid because of the miracles at Nachal Arnon. To cite that Midrash Tanchuma again, which is Rashi's source:

ואף כך בלק ראה מה נעשה בסיחון ובעוג שהיה מעלה להם שכר לשמרו והיה מתיירא מעצמו. ועוד שראה נסים שעשה להם הקדוש ברוך הוא בנחלי ארנון.

The Midrash points to the deaths of Sichon and Og as well as  the miracles at Nachlei Arnon.

And those miracles, while not explicit in the Biblical text, were in fact brought into scope by Rashi on the previous perek:

Concerning this it is told in the account of the Wars of the Lord, "What He gave at the [Sea of] Reeds and the streams of Arnon.		יד. עַל כֵּן יֵאָמַר בְּסֵפֶר מִלְחֲמֹת יְהֹוָה אֶת וָהֵב בְּסוּפָה וְאֶת הַנְּחָלִים אַרְנוֹן:
Concerning this it is told: Concerning this encampment, and the miracles that happened there, “it is told in the account of the wars of the Lord”: when they relate the miracles that happened to our forefathers, they will relate: “What He gave….”		על כן: על חניה זו ונסים שנעשו בה יאמר בספר מלחמות ה', כשמספרים נסים שנעשו לאבותינו יספרו את והב וגו':
What He gave: Heb. אֶת וָהֵב, like אֶת יָהֵב [which is the Aramaic root meaning to give]. Just as from [the root] יעד we say ועד so from יהב ‘to give’ [we get] והב, and the “vav” is [part of] the root. That is to say, what He gave (יהב) them and wrought many miracles at the Red Sea. — [Onkelos]		את והב: כמו את יהב, כמו שיאמר מן יעד ועד, כן יאמר מן יהב והב. והוי"ו יסוד הוא, כלומר את אשר יהב להם הרבה נסים בים סוף:
and the streams of Arnon: Just as we recount the miracles of the Red Sea, so should we recount the miracles that happened at the streams of Arnon, for here too, many great miracles were performed. What were those miracles?…- [Midrash Tanchuma Chukkath 20, Num. Rabbah 19:25]		ואת הנחלים ארנון: כשם שמספרים בנסי ים סוף, כך יש לספר בנסי נחלי ארנון, שאף כאן נעשו נסים גדולים. ומה הם הנסים:
15. And the spilling of the streams that turned to settle at Ar and leaned toward the border of Moab.		טו. וְאֶשֶׁד הַנְּחָלִים אֲשֶׁר נָטָה לְשֶׁבֶת עָר וְנִשְׁעַן לִגְבוּל מוֹאָב:
The spilling of the streams: The Aramaic translation of שֶׁפֶךְ,“spilling,” is אֶשֶׁד -the spilling of the streams, for [there] the blood of the Amorites who were hidden there was spilled. The mountains were high and the gorge deep and narrow, and the mountains were so close to each other, that a man standing on the mountain on one side [of the gorge] could speak to his fellow standing on the mountain on the other side. A road passed along [the floor of] the gorge. The Amorites said, “When the Israelites enter the land by passing through the gorge, we will come out of the caves in the mountains above them and kill them with arrows and stones shot from catapults.” There were clefts in the rock on the Moabite side [of the canyon], and directly opposite those clefts, on the mountain on the Amorite side, there were protrusions, [appearing] like horns and breasts. When the Israelites prepared to pass through, the mountain of the Land of Israel trembled, like a maidservant going out to greet her mistress, and moved toward the mountain of Moab. Then those breastlike protrusions entered the clefts, killing them [the Amorites]. This is the meaning of, “that turned to settle at Ar.” The mountain swung from its place and moved toward the side of the Moabite border, and attached itself to it. Thus, “[it] leaned on the border of Moab.” - [Midrash Tanchuma Chukkath 20, Num. Rabbah 19:25]		ואשד הנחלים: תרגום של שפך אשד. שפך הנחלים שנשפך שם דם אמוריים שהיו נחבאים שם, לפי שהיו ההרים גבוהים והנחל עמוק וקצר וההרים סמוכים זה לזה, אדם עומד על ההר מזה ומדבר עם חבירו בהר מזה, והדרך עובר תוך הנחל. אמרו אמוריים כשיכנסו ישראל לתוך הנחל לעבור, נצא מן המערות בהרים שלמעלה מהם ונהרגם בחצים ואבני בליסטראות. והיו אותן הנקעים בהר של צד מואב ובהר של צד אמוריים היו כנגד אותן נקעים כמין קרנות ושדים בולטין לחוץ, כיון שבאו ישראל לעבור נזעדזע ההר של ארץ ישראל, כשפחה היוצאת להקביל פני גבירתה, ונתקרב לצד הר של מואב ונכנסו אותן השדים לתוך אותן נקעים והרגום. וזהו אשר נטה לשבת ער, שההר נטה ממקומו ונתקרב לצד גבול מואב ונדבק בו, וזהו ונשען לגבול מואב:

I'll just add that it is plausible that Rashi's, and the midrash's, explanation regarding Sichon and Og is not peshat, but is rather derash. That is, Emori could either mean the Emorite people or specific Emorite persons. La-Emori might mean to Sichon or to Og, rather than the Emorite people. Sichon and Og as protectors and warriors, rather than Sichon and Og and stand-ins for the battle with these Emorite people. And this midrashic explanation is non-obvious.

Finally, there is the juxtaposition Rashi makes of לפיכך ויגר מואב. I think that Rashi is grappling with an irregularity of change in topic, that first Balak sees and then Moav fears (much like R' Ovadia miBartenura mentioned). But Rashi isn't making any nuanced diyuk of it, based on Balak not being called a melech. Rather, there is a shift, in that we know that Balak saw, but we don't see Balak's reaction. Meanwhile, Moav's reaction in the next pasuk might be read as a self-contained item -- they feared because of how numerous the Israelites were. That is what was bothering Rashi. Rashi chooses to merge the two in meaning, that the fear was first set into motion by the acknowledgement and contemplation by the Moabites and by the Moabite leadership of the deaths of Sichon and Og, such that they had reason to fear. So pasuk 2 leads naturally towards the reaction in pasuk 3.