My roommates girlfriend wants to stay with us rent-free and I don't want to allow it.
You roommate's girlfriend sounds like she is trying to freeload off of him.
She uses him to get free food and almost nothing of her belongs to him
There is no reason she should be staying at your place without paying rent. She is taking advantage of you and your roommate. This is something you need to have a conversation about with your roommate because it's not fair to you at all.
What do you mean by taking advantage of him.
Your roommate's girlfriend is taking advantage of him by using him for free things, and you should speak with him about it. He needs to know that you're putting your foot down and won't allow her freeloading to reach you.