Who was Balak?
Rashi (4, from a Midrash): He was one of the five princes of Midyan, and when Sichon was killed, Mo'av appointed him king (to defend them against Yisrael).
Ramban #1 (on Pasuk 4) and Seforno: He was a renowned warrior of that time. 1
Moshav Zekenim citing R. Yehudah ha'Chasid: He was one of Sichon''s nobles; then, he saw what Yisrael did to the Emori. This resolves Shoftim 11:25, which implies that Balak did not fight Yisrael, with Yehoshua 24:9, which says that he fought Yisrael! He fought when he was with Sichon; he did not fight after becoming Melech Mo'av 2
Seforno: As is evident from a statement by Yiftach in Shoftim, 11:25. Ramban: And the Torah is telling us that, in spite of that, Mo'av was afraid.
Moshav Zekenim: R. Moshe rejected this. The latter verse calls him Melech Mo'av. This implies that he fought when he was Melech Mo'av! Also, the verse says that he called to Bil'am, i.e. it was at the time that he called to Bil'am (after he became king)! This is not difficult. The verse in Yehoshua is after he became Melech Mo'av.
What exactly, did Balak see that made him afraid?
Rashi #1 and Seforno: He saw how the two kings upon whom they had placed their trust were unable to stand up to Yisrael, and he figured that that being the case, they would certainly not be able to.
Rashi #2: Refer to Devarim, 2:9:1:1*.
Ramban: Because Yisrael was a far more numerous nation than Mo'av, 1 a. since the latter was a relatively new nation, and b. because he heard about the ongoing miracles that Hashem had performed with them and with their forefathers.
Seforno: He saw how a. when Sichon refused to let Yisrael pass through his land, they annihilated him, and b. how their victory did not come about in a natural way. 2