“Now go curse [the nation] for me; perhaps I will be able to war with them and drive them out” (Bamidbar 22:11; compare with 22:6). When Bilam told G-d what Balak had asked him to do, there are several differences between how he quoted Balak and what Balak is quoted as having told him. One of the differences is the word used for “curse.” Whereas Balak used the word “ara,” Bilam used the word “kava,” a term Rashi tells us refers to a harsher curse. Although Rashi points out another change too, and tells us that this change indicates that Bilam hated Israel more than Balak did, he does not tell us this regarding Bilam using a harsher word for curse than Balak. Some (e.g. Devek Tov) are of the opinion that when Rashi says Bilam hated Israel more than Balak he was basing it on both differences, while others do not seem to understand Rashi as referring to both, only the second one.
There is a very good reason why Rashi would not use Bilam’s term for “curse” as an indication that he hated Israel more than Balak, as Balak himself used the harsher term several times (22:17, 23:11, 23:13, 23:25, 23:27, 24:10; see Mizrachi). Nevertheless, the Midrash that Rashi is based on (Bamidbar Rabbah 20:9, Tanchuma 5/8) does tell us that we know Bilam hated Israel more than Balak hated them from the harsher term for “curse” that Bilam used. How can the Midrash say that Bilam hated Israel more based on the term he used if Balak used the exact same term himself?
Maharal (Gur Aryeh) says that even though Balak was fine if a lighter curse was placed on Israel (because he didn’t hate them as much), after G-d told Bilam that he can’t curse Israel using the lighter form (22:12), Balak had no choice but to switch to the harsher form for all future requests. However, since Bilam made it seem as if the reason G-d had refused to let him go was because these officers weren’t important enough (see Rashi on 22:13), it is unlikely that he would have shared with them that G-d said he can’t curse Israel at all. Besides, if G-d had said that Bilam can’t even curse them lightly, surely He wouldn’t allow a harsher curse! Why would Balak think G-d would allow a stronger curse if He had told Bilam that he can’t even curse them lightly?
Toldos Yitzchok asks several questions on this part of the narrative, with his sixth (of eight) group of questions being why G-d used the weaker term for “curse” in His response if Bilam had used the harsher one, as well as why Balak switched from using the weaker term to using the harsher one. He suggests that for Balak’s needs, a lighter curse would have been enough, so that’s all he asked for. Bilam, knowing that G-d loves Israel, was afraid that when he asked to curse Israel, G-d wouldn’t let him. Realizing that if he asked permission to place a lighter curse on them and G-d said “no,” he surely wouldn’t be allowed to place a stronger curse on them, he therefore asked permission to curse them strongly, leaving wiggle room to be able curse them lightly even if he was denied permission to curse them strongly. G-d saw through his scheme, and answered Bilam by telling him that not only can’t he place a strong curse on Israel, but he can’t even place a light curse on them. After Balak’s initial request was denied, he sent a larger number of officers, and higher-ranking ones, hoping that their status would change G-d’s mind. However, fearful that he would again be denied, this time he asked for a stronger curse, leaving room to ask for a weaker one afterwards. [I changed a couple of the details slightly to avoid questions that could be asked on this approach.] Bilam’s response to Balak was that this scheme wouldn’t work, as he couldn’t transgress G-d’s word, whether “to do a small thing or a large thing,” i.e. a small curse or a large one.
Putting aside the other issues with this approach (such as how they proceeded if both knew full well that G-d wouldn’t allow any kind of curse, Balak’s request still being referred to with the weaker term, see 23:7, and G-d denying permission to place a harsher one, see 23:8), since Balak continued using the harsher term for “curse” even after this exchange (23:11, et al), his choice of terms would seem to have nothing to do with trying to leave room for a weaker curse. As far as our issue is concerned, though, if Balak used the harsher term so that a weaker curse could still be placed, doing so would not indicate his having as much hatred towards Israel as Bilam did. Nevertheless, the same can be said for Bilam’s use of the harsher term (i.e. that he used it to leave wiggle room, not out of intense hatred), and yet the Midrash (which Toldos Yitzchok references in his question) says that the harsher term does indicate a stronger hatred.
Chasam Sofer (Toras Moshe) suggests a similar (if not the exact same) approach, and asks why Balak, if he didn’t have the same hatred for Israel as Bilam, continued to use the harsher term for “curse” even after realizing that there was no wiggle room. He suggests that since Balak was an even greater sorcerer than Bilam (see Tanchuma 4/6), he knew that Israel would be punished via the term for a harsher curse (Q-B-H), so, after realizing that trying to curse Israel without referencing this impending punishment wouldn’t work, he insisted on using that term. What Balak really “saw,” though, was the sinning with the Moabite women, where the same word is primary (see 25:8). If Bilam used the harsher term because of his hatred of Israel while Balak only used it because he thought it was a necessary part of bringing about any kind of curse, there is no issue with Balak using the same term as Bilam without equating their level of hatred.
The Rosh is among the commentators who explain Balak asking Bilam to curse Israel “for me” to mean “even though it means I will also be cursed,” as whomever curses Avraham’s descendants (referring to those who also descend from Yitzchok and Yaakov) will be cursed themselves (B’reishis 12:3). In other words, despite knowing that he will suffer because of it, Balak was willing to endure personal suffering in order to curse Israel. By limiting his “curse” to a lighter form, though, he was also limiting the curse that would boomerang back to him; his hatred of Israel wasn’t strong enough to suffer more in order for there to be a stronger curse on Israel. Bilam, on the other hand, hated Israel so much that he was willing to endure more intense suffering so that he could place a stronger curse on Israel. But this comparison only applies the first time each used the word “curse.” Once Balak heard Bilam use the harsher term (even if was in the context of G-d not allowing him to curse Israel when the request came from such low-level officers), he knew that Bilam hated Israel more than he did (and was willing to endure harsher suffering in order to harm them more). Not to be outdone, Balak started using the same term; not because he hated Israel as much as Bilam did, but because he didn’t want to seem as if he was unwilling to make the same personal sacrifice that Bilam was willing to make.
Similarly, it can be suggested that once Balak heard Bilam use the harsher term, rather than seeming out of place because of his less intense hatred of Israel, Balak decided to use the same term for “curse” that he heard Bilam use. Alternatively, in order to find favor in Bilam’s eyes, once he realized how much Bilam hated Israel, he used the same term as Bilam even though his hatred of Israel was not as strong. Either way, because Balak initially used the lighter term for “curse,” we know that his hatred was less than Bilam’s, even if he subsequently used the stronger term.