george arrives at the keller wearing his fathers hat. what is the significance of this?

This seems ironic as George describes his father as “a little man” and a sucker. I think it really symbolizes that George feels he has become the head of the family.

The significance is: when someone wears somebody else's hat, it means that he identifies with him. In this case, George identifies with Steve, because he has just heard what an injustice was done to him. He feels sorry for him, and that's the meaning of wearing Steve's hat.