The US military is currently accepting recruits with autism, as long as it doesn't interfere with duty or training. Or something like that.
Frankly, mild autism is an asset in the military. It's an environment where the rules don't have to make any sense; they just have to be followed.
There are a lotvof mentally ill people in the military.
Seeing autism as a mental illness I suppose is a perspective that is more widely shared and debatable, but what does being overweight have to do with anything?