Stand by thy burnt-offering - We have already seen that blessing and cursing in this way were considered as religious rites, and therefore must be always preceded by sacrifice. See this exemplified in the case of Isaac, before he blessed Jacob and Esau, Genesis 27 (note), and the notes there. The venison that was brought to Isaac, of which he did eat, was properly the preparatory sacrifice.
Balaam apparently expected to mark some phenomenon in the sky or in nature, which he would be able, according to the rules of his art, to interpret as a portent. It was for such “auguries” (not as the King James Version “enchantments” Numbers 23:23) that he now departed to watch; contrast Numbers 24:1.
An high place - Or, “A bare place on the hill,” as opposed to the high place with its grove of trees.