I just don't know

My current boyfriend knows about my ex who was an alcoholic. And he keeps bringing to my attention his I guess you could call worry, and curiosity as to my feelings when it comes to him and I because I guess he drinks more that what I assumed. He told me he drinks every night, I quote "it's not as bad as it used to be" "I have just recently been adding all these new clubs and acirivites because of how you feel about it" I asked him if he'd ever hurt me and he said "no I'd even stop completely if you asked me" I just don't know what should I think? Should I worry because I am. I told him I refuse to fall into another relationship like my last. Does anyone have a similar experience or some educated advice they would be willing to share?