Most Helpful Girl
Are you guys exclusive? If not then you can't really tell him to stop, especially if he's not acting out of line when drunk. However, you might want to consider if you even want to continue dating him. If you guys are casually dating and something like this is already bothering you, then you're going to eventually need to confront him on it when you guys do go exclusive and have something change.
Otherwise you guys are going to break-up fast because you're going to be constantly annoyed and he will catch on. Drinking sounds like something that he enjoys so it might not be fair of you to take that away from him. But if he truly wants your relationship to work then he'll be willing to compromise. If you guys are casually dating, then maybe he's not the right guy for you since this seems to be somewhat of a deal breaker for you. However, you can't really tell him to stop because you don't have the right yet. He's not committed to you. If you guys are exclusive, then you have the full right to tell him how you feel and ask for a change. If he really likes you, then he'll try to make you happy but if not then it's okay. He's just not the right guy for you.