Listen to yourself and what you need. You have no responsibility to carry your boyfriend, especially after he has repeatedly shown he is not trustworthy at this time. If he becomes depressed because you kick him out/leave him, maybe next time he will think harder before relapsing with someone else. No one has a gun to his head forcing him to steal money/give in to his addiction. We all have difficult problems but it does not look like he is facing his. He does not have enough personal integrity to be your partner right now. I would kick him out/leave.