The most telling description of Curley is given to George by Candy in Chapter Two of the short novel in the following two direct quotes.
"That's the boss's son," he said quietly. "Curley's pretty handy. He done quite a bit in the ring. He's a lightweight, and he's handy."
"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?"
Throughout the rest of the story Curley's behavior is in keeping with Candy's wise assessment of his character. Curley has an inferiority complex because of his small size. In attempting to compensate, he has trained to be a boxer and has developed an aggressive personality. No doubt he goes in for body building along with the kinds of exercises that boxers typically engage in, such as jogging, bag-punching, and rope-skipping.
His wife appears to be a very young girl, possibly only sixteen. Such a marriage would seem to be in keeping with Curley's inferiority complex; he might feel inadequate to relate to an older woman. He is extremely jealous and possessive because he senses his bride does not love or respect him, which happens to be true. She only married him to escape from her home where, like many another teenage girl, she wasn't getting along with her mother.