I think it means he knows that he gets drunk, and he's trying to outgrow the fact that he drinks too much because he knows his girl isn't very happy about it and it hurts her.
"So when I come back, I won't say a word, I know, I've said this before, Don't speak, liar."
He feels bad about drinking when he knows the girl hates it when he comes home to her drunk so early in the morning/late at night, so he promises not to say a thing to her because. Well, you know how people are drunk. And he knows he's said it before but he's trying to keep his promise.
I'm missing something at the end, but that's more of a "feel for yourself" interpretation part of the song. ^w^' Sorreh.