Would you toss out FDR? Churchill? Stalin?

FDR had had polio, and was actually wheel-chair bound. Churchill and Stalin were also obviously overweight. And God alone knows how many leaders of the past smoked (e.g., Fidel Castro, Winston Churchill). Eisenhower had a heart attack while President, Kennedy had back problems.

Mental problems, no, I don't want such a person to lead. Physical is irrelevant (unless they affect mentation).

(And let me note two fictional characters who are grossly overweight but fully capable mentally: Mycroft Holmes and Nero Wolfe.)