I wasn't able to find any studies which looked at the relationship between a candidate's body shape or physical fitness and their predicted election success. The closest source I could find were unfounded claims that fitness helps the perception of leadership. Related key-words I'm not directly interested in include health perception, attractivity, anti-fat bias and appearence.
There is significant evidence that voters are more inclined to support politicians who are attractive. A study in Finland for example asked people to judge the attractiveness of thousands of Finnish politicians. They found that "an increase in our measure of beauty by one standard deviation is associated with an increase of 20% in the number of votes for the average non-incumbent parliamentary candidate." This is likely due to what's called the "Halo Effect," a cognitive bias where we tend to believe attractive individuals are also smarter, more capable, and all-around better.
From there it's not difficult to draw a line from attractiveness to fitness. Studies find people tend to find fit and thin people more attractive than fat people, at least in Western society.
So while I don't know that any research has been done into the effect of a politician's physical fitness, it's probably safe to assume vicariously that good fitness has a positive effect on electability.
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.