Contrary to popular belief, nobody looks down on others in a gym. If you're there it shows will to improve, so it shouldn't be awkward. Also, obesity is not the only form of poor physical health.
Not quite my thing, but it doesn't hurt anyone. Don't see anything wrong with it. Also, the term lolicon refers to the sexualization of kid characters. If it's not sexualized, it's not lolicon. I don't know if that's the case with Full Metal Panic.