Literally it means 'to put a harness on yourself', like упряжка. Figuratively it's a slang word that means you are putting in a lot of effort or taking on an obligation, in this case: Why are you 'white knighting' for this idiot girl? Why are you defending this idiot girl so much? or Why are you so worked up over this idiot girl? Чо, чё, чиво, што, шо, штаа, чтаа are many bastardized variations of что you might see on the internet. They're all slang, including asking чего to show your bafflement, though чего is a polite word.

фу.... где вы это услышали? В фильме?

Although I'm a Muscovite born and bred, I've never heard that phrase before. The meaning, though, is quite transparent. Marina in her comment above explained it really well. Anyway, most definitely I wouldn't recommend using it. Sounds so rude to me. It could be criminal slang or something...

Do you defend this stupid cunt?

I would add. This phrase sounds very rough and come from commoners or criminals. That the way gangsters or brudes say. Yes, Marina is right about its meaning. Also, I like to write "чо" instaed of "чё" (equal meaning = что), because it assosiated to me the way cute guys (maybe a lil bad streets boys) speak. It is just a trick.