Insecurity, meanness, and cowardice are Curley's three main traits.
Curley's insecurity seems to come from his size. When George and Lenny are introduced to Curley, Curley immediately begins to pick a fight with Lennie. Candy explains that Curley is always picking fights with bigger men. Curley needs to prove himself physically and chooses opponents larger than he is, which is part of his cowardice.
The reason this is a cowardly move on Curley's part is this: if the larger opponent wins the fight then he is just seen as picking on a smaller man. It's not a fair fight. If Curley wins the fight, he has done something impressive. The situation is unfair to the larger man, as we see with Lennie when he is forced to defend himself.
We see Curley's insecurity also in his behavior toward his wife. Curley is constantly searching for his wife because he is apparently afraid that she will cheat on him with one of the other men. He cannot trust her due to some lack in himself. This notion is rather clearly made in the text as George discusses Curley in the bunk house.
Curley never picks a fight or argues with anyone who is on his own level but always seeks to punish those beneath him. This is part of his meanness. This point is made clearest when Curley tries to beat up Lennie without reason and hits Lennie repeatedly when Lennie, at first, refuses to retaliate.
Curley is not a complex or complicated character. He represents a meanness of the larger situation that these men find themselves in, doing hard labor for bosses that do not care about them and, in Curley's case, only want to prove something about their superiority.