Maybe it's from 회를 치다 and that originally means you actually slice raw fish and eat.
However, if someone does it to you, that means he maybe asks for things like lending money, doing things for you and so on...
So, the speaker says it maybe to warn the listener that he will not stand it anymore.
회쳐먹다, 떼먹다, 튀다, 등쳐먹다 등등 they are similar.