This phrase has a few different meanings. It could mean that you're letting loose and having some fun you know, just going ham. Just like raging out at a party or something. However this phrase could also mean just going the hell off on someone for a stupid or non-apparent reason.
Basically a random outburst of either positive or negative actions.
Dude, me and Ray were breakin' weird last night at that party. It was awesome!
Dude, Mrs.Cockburn broke weird on Ray today in class for sharpening his pencil too many times.