Should I refuse to pay my roommate for internet?
Why won't you pay your share of the internet?
He claims that I can't use the internet at night because he's sleeping
You should compromise on the internet time and ask him why he doesn't want you using it at night. If you don't pay your half then you don't deserve to use it.
Not a chance, I don't use the net that much and I'm going to teach him a lesson by not paying for internet.
Even if you don't use it a lot, you still are and should take responsibility for some of the costs. It may not feel very fair to him, so how about making a deal instead of trying to get back at him?