When Balak summons Bilam, he says, "For I know that whomever you bless will be blessed and whomever you curse shall be cursed." This implies that Balak understood that Bilam's main strength was in blessing people, and the secondary strength was in cursing.
If that's the case, and he feared the Israelites, why didn't he request Bilam to bless him and his own nation Mo'av to be successful and to feel safe against the Israelites, if he feared their conquering him. Or, if they were to wage war, he could have asked Bilam to bless Moav with the ability to win the battle? Why, instead to he resort to Bilam's ability to curse?
In his weekly drasha. my rav used this to explain / prove the historical "focus" that anti-Semites have had for millennia. IMO, that makes for a nice drasha, but it doesn't explain, really, this situation. I don't think Balak was motivated to destroy Israel because of hatred. It seems that he feared their overtaking his land, even though, we know that God had told Israel not to wage war against Moav. (See parshat Devarim.)