Glad you are here and sharing Hopeful. There's really nothing positive about the situations that active/drinking alcoholics put themselves in - not to mention others around them.
And there is definitely a gray/fuzzy line between helping/supporting and enabling. If you are paying all his bills and he's still drinking despite your repeated attempts to help then it probably is enabling to be quite frank.
Right now I would suggest you try and focus on helping yourself - if you are keeping this all inside it's potentially a form of co-dependence. I would personally suggest letting someone in your family know who you can trust...you needn't go through this alone. And as far as how you bring it up, just be honest - my boyfriend is an alcoholic and he won't stop drinking. There is no shame it telling the truth.