At 16 I don't think you should have to worry about weights too much in general. As long as you're not too hardcore I'm sure it wouldn't hurt. The push ups and sit ups are definitely good. As far as how it effects boxing I can't answer you truthfully. Hopefully someone more qualified will post. Your trainer at the Gym would definitely know more than I. I wrestled most of my life so training was vastly different. I should have boxed too. Oh well