Only married for a couple of weeks, Curley has taken an adolescent bride and, according to Candy, the old swamper, he is now "cockier'n ever since he got married." Now, Candy says, Curley wears a glove on his left hand that is filled with vaseline, which he has purportedly said is to keep his hand soft for his wife.
They say that the glove is filled with Vaseline and is worn to keep his hand soft. He wants to keep his hand soft for his wife, which refers to intercourse. The glove is mentioned again and they assume Curley has also changed his diet and is taking medication for his wife.