Well, it's a tough call. I wouldn't necessarily dump someone because they are sometimes nuts.
It sounds to me like you have taken on an almost 'mothering' role with him. You aren't responsible for him being lonely, although I would feel a lot of sympathy if I had a friend like that, his happiness is ultimately his responsibility. Maybe if you like him and don't want to break with him, lay down a few ground-rules with yourself. I wouldn't collude with the paranoia, i.e. if he asks you to prove yourself in any way, don't. He won't believe you anyway by the sounds of it.
"Well I managed to cut him off for a couple months a while back, but then he called my house and the whole cycle started all over again".
How did you feel when you cut him off for a few months? If you feel better off when he's not around, then that will tell you a lot about how you really feel about the situation.