You've given us very little to go on. Is Kid Nickels guessing that K'nuckles' buddy is named "Backchap"? That will be my assumption here.
Anyhow, it sounds to me like K'nuckles is suggesting that his buddy Backchap is having a problem, but if everyone allows Backchap to cry for a while, Backchap will put this problem behind him. I believe that there are lots of roughly parallel expressions like this. When I was a kid, macho people would respond to pain by "walking it off," walking until the pain subsided. A drunk could "sleep it off," sleep until (upon waking) he would find himself sober. I could go on, if you like.
So here, K'nuckles is responding to the question "But what about your buddy?" as if that question meant "Should we do something to help your buddy?" And he's responding "No, just let him cry and he will get over it."