Curse me this people, i.e. curse them for my sake and benefit; use thy utmost power, which thou hast with thy gods or infernal spirits, to blast and ruin them. That we may smite them; thou by thy magical imprecations, and I by my sword joined with them. He had some experience of, or, at least, a great confidence in, Balaam's skill and power in these matters.
Related Commentaries of Numbers 22:6
Numbers 22:6
6 Come now therefore, I pray thee, curse me this people; for they are too mighty for me: peradventure I shall prevail, that we may smite them, and that I may drive them out of the land: for I wot that he whom thou blessest is blessed, and he whom thou cursest is cursed.