How do we know that Curley is suspicious of his wife?
In Steinbeck's Of Mice and Men, Curley wants control over all those who are below him: the ranch hands (namely Lennie) and women (his wife).
First, Curley doens't even name his wife. She is simply his: "my wife." Even the other men call her "Curley's wife." She has no identity of her own. To call her by name is a loss of control for him.
Secondly, Curley is constantly looking for her in the bunkhouse. This is a sign that he doesn't trust her around the guys. George knows this, and he warns Lennie several times to stay away from both Curley and his wife. Curley asks Slim if he's seen his wife because he suspects she is having an affair with Slim. Knowing he will get whipped by Slim, Curley starts a fight with Lennie instead.
Remember, Curley suffers from a Napoleon Complex:
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.
Not only has an inferiority complex around the guys when it comes to size, but he also has one when it comes to sexual prowess. He keeps his hand in a glove of vaseline, saying he's keeping it soft for his wife, as a means to lord over the other men that he not only has a wife (and they don't) but that he has control over her. His boasts suggest that Curley wants to confine his wife to the bedroom only, that she is a domestic plaything who doesn't belong in the public group of men.