You have a perfect right to be leery and no, you are not being "controlling" for not wanting to be in a relationship with someone who has an addiction. Things will not get better if you marry him and could possibly get worse, what's in it for you? It isn't about dictating his life, it's about your own life and the kind of person you want to be involved with. The drinking is an issue for you and he doesn't want to or can't address it... now you know how seriously your concerns are being taken (i.e. not at all).
My exbf used to drink to cope as well, every problem that came up in life would have him running to the bottle. That is not healthy and eventually it came back to bite me in the a** and he was abusive and defiant, as well as sneaking around doing things behind my back. Not exactly the foundation of love and trust a relationship should be built on. Personally I could not go along with it, I thought he was killing himself and taking me down with him. The end of our relationship was excruciatingly painful but I believe I am on the road to a better life. He wanted to drink, a LOT and I do not miss wondering what bar he is at or if he would die of liver cancer.
I was married once before and someone else's bad decisions can ruin your finances & credit rating. I would not go down that road with an alcoholic, EVER.
Do yourself a favor and educate yourself on the disease of alcoholism, it is progressive and there is nothing you can do to control it or cure it.