There are three ways in which Curley adds to the tension of the story.
First, no one likes Curley. In fact, his wife who has been married to Curley for two whole weeks does not even like him. The men of the ranch also dislike him, and the only reason why they put up with him is because he is the son of the boss. So, whenever he is around, there is tension. Here is an example:
I don’t care if you’re the best welter in the country. You come for me, an’ I’ll kick your God damn head off.”
Second, Curley, being a small man, feels the need to prove himself. So, he likes to talk big and challenge bigger guys. This means that he want to bother Lennie and challenge him. At one point, he beats on Lennie, until Lennie fights back and hurts Curley.
Third, because Curley's wife cannot stand him, she looks at the other men. This makes Curley jealous and even more suspicious of the men. As she spends time with Lennie, Lennie accidentally kills her. This creates the greatest tension, because George knows that the men will kill Lennie.