I'm going to say my best friend's boyfriend has a drinking problem, at least I want to say something, what do you think?
What makes you think he has a problem?
It's because I overheard them talking about it
If you overheard it, that means they didn't tell you directly.  Since that's not the case, it's not your information to share.  People's personal issues aren't to be discussed without their permission.
But, I'm her best friend. Of course I should get involved!
I don't really think that it matters that you are her best friend. All you did was overhear a conversation that didn't involve you. In fact, if you do say something, your friend might accuse you of eavesdropping and get upset with you.