Yeah, he might be annoying, but he is 16 years old. Half of the responses are really stupid jokes like "punch him with a dumbell" or whatever.
OP, I don't know the reasons why you go to the gym, but I assume one of the most important motives is because you wish to improve yourself. Well, in front of you is the opportunity to be a better human being; to be the bigger man.
Confront him, peacefully. No swearing, no losing your cool. Ask him politely if there's something about you that bothers him. He will most likely give you some half-assed rude response, but you need to get over that pride, and try to understand him. Maybe he is being bullied in school so he doesn't go (which would explain why you find him there at those times) and finds consolation in giving some guy a hard time. I have no idea, but he is a human being, and you should treat him as such.
If your efforts turn out futile, then yeah, you can go and have him kicked out. But you got the chance to make someone's life better.
You can smell the resentment of the people commenting here. You are all reinforcing the stereotype of gym goers being close minded and aggressive.
Don't let that get to you. Help him
You can improve both of your lives. Do the right thing. It may not work out, but you will have tried.