We have a case similar with this, in Bellevue, Nebraska (home of the world-famous Strategic Air Command).
There's a police officer, who's 5'9" and weighs, easily, 350 pounds.
He was let go after he failed the physical-endurance tests.
He's not an old guy, either, probably circa his mid-30s.
So he sued the city of Bellevue, to get his job back.
It doesn't look like that's going to happen, though.