When Romeo says, "I beseech thee, youth, / Put not another sin upon my head, / By urging me to fury: O, be gone!" (5.3.61-63), what is he threatening to do to Paris? What was Romeo's other sin?

In these lines Romeo is threatening to kill Paris, and his other sin is to have kissed Juliet.

Explanation:

In this scene we find Romeo in a fight against Paris. He warns him that he does not want to fight, but that if necessary he will defend himself and will have to kill him.

Romeo always sought peace with Paris but Paris decided to fight anyway, and Romeo had to kill him. This was what produced his exile.

On the other hand, the other sin that Romeo has was having kissed Juliet. Let's remember these lines:

"If I profane with my unworthiest hand

This holy shrine, the gentle sin is this:

My lips, two blushing pilgrims, ready stand

To smooth that rough touch with a tender kiss. "

That would be his other sin.

the conclusion would be the most affected category scoring

buenas noches would be your answer