I would understand wanting him to pay up if he is eating your food or turning up the heat when nobody else is home, but all of the things she is citing either cost her no money (somebody sitting on your couch a couple of times a week is not going to cause enough wear and tear that you'll have to replace it imminently) or are totally negligible costs. How much water does a couple of glasses a day cost you? I would be pretty annoyed if my roommate's partner sat on the couch and watched my TV all the time, but this doesn't sound like that's what's happening.
I have to wonder if this girl ever has her friends over to hang out. Not all of my roommates have boyfriends or girlfriends, but we all use the communal space to host friends pretty regularly, and nobody has a real problem with it. I would be much more annoyed if my roommate invited 10 friends over every week and monopolized the living room all day on Saturday and Sunday than if she invited her boyfriend to sleep over a couple of times a week. If you are dating and you both have roommates, it shouldn't be a crime to sleep over at each other's houses a couple of times a week.