The Army is similar - they have to meet certain height and weight standards but I am one who believes that if a Soldier can pass a PT test (with at least a 250 score) and can ruck a 50lb ruck march for 4-5 miles then I think the Soldier is good enough for me regardless of their size.
I must say though, being around the Naval Base here, Sailors and Airmen are fatter and more out of shape than Soldier. I just can not see how they get by.
When I joined the USAF back in 1994, we were the only branch that had a lift requirement at MEPS It was (something like) 45lbs to chest level. (I believe the Marines had their recruits do some physical stuff at the recruiters office at the time) My entire time in they "taped" us to check for body fat. I spent most of my career fighting to get off "weight management" or fighting to stay off of it. It sucked because I was fairly fit and didn't look as bad in uniform as some others that never had a problem using the "tape". They also made us ride an exercise bike once a year, but that was easily defeated by, ironically, smoking a cigarette right before the test (something about heart rate). After I got out, I think sometime in 2002 maybe, the AF dropped all of that and now everybody runs biweekly just like the Army. The fit tests include pushups, situps and a run. A smoke ain't going to help you there
But yeah, generally speaking, the AF and Navy are a bit more out of shape than the Army and the Marines. We don't need to be.
(there are a lot of restrictions for a lot of specific jobs in the military too. No chicks on subs. No big dudes or little dudes in fighters. Few chicks in Special Ops. No straight men in the Navy.)