Season 2 Kenny seems a lot happier now that he's got Sarita, huh? No longer the depressed alcoholic he became when Katjaa and Duck died, right? And what exactly would cause this new, happy Kenny to cry and get drunk again? Sarita's death, of course. Can't really think of anything else.
It could be crying after Sarita's death, but that would be season 1 all over again. It can be him crying from pain after being horribly tortured by Carver. And then he would get drunk to forget about the pain.
"the only thing sucks in ck2 is my daughter sister on the me dick" - Cackman
It could be the drawing of Kat and Duck, as Jake said, but it could also be a non-canon death, for the cry. As for the drunk, remember "WE ARE SCREWED! If this isn't the time to get drunk, I don't know what is." Or whatever he said, he might lose hope after getting the shit kicked out of him by Carver.