Damian isn't used to drinking --- it was never a social activity he found interesting enough or even valuable. So it's no surprise, the fact that he has 0 tolerance once alcohol gets into his body.
Again and again he complains about being helped to the couch in the Manor's living room, after a gala in which he decided to drink. But the truth is, although he could've made it on his own, his whole world would've been spinning.
"You know, I was lying when I said you looked beautiful." Damian says seriously as his head tilt back, but before you can feel offended, he adds, "You don't look just beautiful --- you are breathtakingly stunning."
He's drunk, as hell... but he seems completely aware of what he's saying, even if his voice has a bit of a drawl.