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Curley is the son of the ranch boss, so he's got a big head—which doesn't quite match up with his body. He used to be a lightweight fighter, and he just can't let go of the life: he picks fights just to prove himself on the ranch among other bigger (and better) men.
Candy lays it out for us:
Well . . . tell you what. Curley's like a lot of little guys. He hates big guys. He's alla time picking scraps with big guys. Kind of like he's mad at 'em because he ain't a big guy. You seen little guys like that, ain't you? Always scrappy? (2.91)
Stereotypes aside, what we see here is another character who—like Lennie, Curley's wife, or Crooks—is defined by appearances. Lennie is big and therefore dumb; Curley's wife is a woman and therefore untrustworthy; Crooks is black and therefore inferior; Curley is short and therefore "scrappy."
It doesn't help that his wife has the "eye": he's married to a woman he wants to control and can't. While he brags about his sexual prowess to others, his constant fretting about where exactly his wife is show us that, for Curley, sexual power is a way to show his masculinity. In other words, size isn't everything.
Unfortunately, for Curley it is everything. He obviously lacks sexual power, and so he shows his strength other ways—like, by picking on the slow and weak Lennie. And he's got a good system down, too. As Candy explains, "S'pose Curley jumps a big guy an' licks him. Ever'body says what a game guy Curley is. And s'pose he does the same thing and gets licked. Then ever'body says the big guy oughtta pick on somebody his own size, and maybe they gang up on the big guy. Never did seem right to me. Seem like Curley ain't givin' nobody a chance" (2.93).
In other words, Curley wins even when he loses—until the end, when George kills Lennie. You might think that Curley's "lost," since his wife has just died. But he gets to go out and hunt down his wife's murderer: how much more masculine can you get? By killing Lennie, George takes away Curley's control of the situation. And the best part is that Curley doesn't even realize it.Curley Timeline