Yeah, I'm sure Hooters has been down this road a few times before and know exactly what they're allowed to do.
On a related note, I also have a job that requires me to maintain my weight within standards and pass a fitness test twice a year, a test that requires me to run 1.5 miles within a certain time and do a certain amount of situps and pushups. And these days my Navy is cracking down on fitness failures, showing them the door.