My middle kid, now 15, repeated 2nd grade. Though our circumstances were a bit different, she is also small and she was immature.
She attended a school from PreK through 2nd where the birthday cutoff was end of calendar year. She then switched to the public school which has an end of September cutoff (birthday is in October).
While she did know a few kids at the public school through rec sports, I don't think any of them knew she was repeating a grade. She could have gone to 3rd - public school said she was ready academically - but left the decision to us. For social reasons, we chose to repeat 2nd.
Around here, most rec sports are grade based, but we only made the mistake once, just one sport, one season, of putting her in with grade mates (this is prior to the repeat year). She is not a natural athlete, and we didn't think she would even play rec sports beyond the age of 12. However, around that age, she expressed interest in playing travel softball, and started playing volleyball for the school because a friend asked her to go to tryouts.
She is now in her 3rd year of travel softball, made JV volleyball at school (got a good amount of playing time), and is a practice player for a club volleyball team (can't commit to play tournaments due to softball conflicts). She is not big, but did finally grow, and is now 5'-4" and almost 100 lbs.
Your son could play pound football until he reaches HS age so he isn't greatly outsized. Baseball is great for kids of all sizes - we have seen a lot of softball as our older two both play, and there are tiny kids to huge kids who are great players.
I realize that our situation is different due to the school switch, and I will note that she was bored in elementary, though she is not the type to complain about it. Good luck with your decision.
