Curley's hatred of "big guys" comes from his own small stature. This is a reflection of his own insecurity and his own experience as a boxer. Consider how Steinbeck describes the first time Curley sees Lennie and George:
He glanced coldly at George and then at Lennie. His arms gradually bent at the elbows and his hands closed into fists. He stiffened and went into a slight crouch. His glance was at once calculating and pugnacious.
Curley holds an antagonistic element towards those who are bigger than him in terms of his own insecurity in being of a small stature. Additionally, his own background as a boxer is one where he authentically believes that he can "lick" anyone who is bigger than he is. It is for this reason that he has a dislike of those who are bigger. Additionally, given his own small stature, he feels threatened that his wife will find a bigger guy more attractive than him, another insecurity that he has.