Or HaChaim on Numbers 22:8/אור החיים על במדבר כ״ב:ח׳

1 לינו פה, "stay here overnight." Bileam may have meant that the messengers stay overnight in his own home, and that is what he meant by the word פה, "here." He concluded by saying that he would tell them what G'd was going to say, כאשר ידבר, not what G'd had said. He hinted that by staying overnight at his home he could inform them immediately G'd would give him instructions. When he emphasised הלילה, "this night," he might have inadvertently revealed his miserly nature as he was not willing to play host to them for more than one night.