I'm not aware of any studies that directly address physical fitness in elected leaders, though anecdotal evidence would tend to suggest there is little correlation. Trump is dramatically overweight, Obama and W Bush were fit but not buff, Clinton was fairly chubby during his administration, HW Bush was nerdy; and let's not get into the physical fitness of Congress, which is clearly a steak and potatoes crowd... The closest fit I can recall are studies that show that taller candidates have a distinct advantage at the polls, and that voters prefer candidates who are 'businesslike': attractive, but not beautiful or stylish; serious, but not overly intellectual or dramatically opinionated; good-natured, but not jokey or clownish. Excessive qualities tend to make voters nervous.
It's worth considering the case of Paul Ryan, who was the last national-level politician I can recall who made a point of emphasizing his workout regimen. That aspect was largely treated like a joke, even among his supporters: a general eye-roll at Ryan and his muscle shirts. I suspect it's a kind of vanity that people don't expect (or like) in leaders.