@Kenneth12 At this point, I'd sit the guy down, tell him that the time to have mentioned that he'd like his girlfriend to come over or spend the night was at the time of booking, rather than springing it on you after he arrived, and that now if he would like her to be able to come and go as she likes, that he needs to pay xx extra for the remainder of his reservation (not according to exactly how much time she spends there, but a set amount). You could hopefully do this in a non-confrontational, " Seeing as how you don't have much experience as a guest, you probably didn't realize this, but..." way and hopèfully it won't go sideways.
From your post, it sounds like he did mention when he booked that he was going to be visiting his girlfriend, so I wonder why you didn't ask him at that point if he was aware that unless he paid for a additional guest, he couldn't have her over. Maybe you were focused all his other cluelessness and thin profile and it didn't really register that he might try to pull this?