Dena Pishra writes that Achashverosh and Haman sat down to drink to finalize their deal.
Eyney Ha’Eyda, on the other hand, writes that Haman here attempted to get Achashverosh drunk to keep him from changing his mind, as he is liable to do. Perhaps this is one of the reasons we drink on Purim.
The fact that Achashverosh is drinking at this point is one of Malbim’s strongest proof that he did not know what was going on. Otherwise, he should worry at least, but certainly not have a drink!
R’ Moshe Dovid Valle brings a proof against the idea that Achashverosh was blissfully ignorant of Haman’s plans. He notes that the gematria of Haman (5+40+50=95) is equal to “hamelech” (“the king”) (5+40+20+30=95). Therefore, he writes, they were equal in their evil and equal in their joy.
R’ Dovid Feinstein quotes the Talmud (Sanhedrin 63a) that the Jewish court is not allowed to eat on a day it passes the death sentence on someone. The reason for this is that the court should not celebrate the taking of a human life. The fact that Haman and Achashverosh are drinking at this point is evidence that they are cheerful, thinking that they are doing the world a favor. Like many evil people in history, they allowed their good intentions to perform the worst of actions in the Machiavellian delusion that the ends justify the means.
The Midrash (Esther Rabbah 7:21) writes that this drink-fest is a consequence of Yosef’s brothers sitting down to eat after throwing him into the potentially deadly pit (Bereishis 37:25). In one view, the entire Purim story is a tikkun for the sale of Yosef. The only reason we could be punished for the sins of our ancestors is if we continue to repeat the same mistakes (Rashi to Shemos 20:5). The main sin of the brothers was that they lacked love for their brother. Again, this is why unity is one of the themes of Megillas Esther.