Peter didn't drink enough to have a good estimate of how much it took to get drunk, and his lack of tolerance didn't help. Sirius probably seemed more drunk than he was because there weren't really any inhibitions to break. He put his arm around Sirius, assuming that he needed help standing up. Perhaps he was drunker than he'd let on.
"Full moon's coming up. I wanted to get some rest, since we'll be out all night." Peter yawned again and thought back on his dream. It was harder to remember than it had been a few minutes ago, but the more he tried not to think about it, the more he remembered. "So what are these better things of yours?"