If you're really concerned with your kid's heath, you can make an early morning or late day apt. We use kaiser and they have apts as early as 8:30am and late as 4:30pm. Physicals only lasts an hour, which should give you plenty of time to get him back to school/work or pick him up after school to go for just 1/2 day.
Lots of good advice about just focusing on eating more healthy and exercising. I was a chubby teen. Didn't learn good eating habits or nutrition till my college years. I went up to 165lb at 5'3" as a teenager. I went back down to 120 when I was in my mid 20s with a lot of exercise and cutting out most junk. It's never too late, but good that you're becoming more conscious of it and be more thoughtful moving forward.