This guy doesn't exactly deal with his wife's infidelity with a stiff upper lip. We meet Curly at the very beginning of the movie, when Jake presents him with photographic evidence of Curly's wife's adultery. (Curly hired Jake to see if his wife was cheating on him).
Naturally, he takes it pretty badly, and disappoints Jake by being unable to pay him in full. Later in the movie, Jake pretends to lead the police to Evelyn—but he's actually going to Curly's house to ask him to drive him out the back, so he can escape and confront Noah.
When he knocks on the door, Curly's wife answers, bearing a black eye indicating that Curly hit her for cheating on him. Even though Curly agrees to help Jake (since he owes him money), we get a sense that he's not such a great guy, given that he beats his wife and that he hired Jake as a private eye without being able to pay him…
Fun fact: Burt Young went on to play Adrian's brother in Rocky. Guess he made a living out of playing not-so-nice guys.