I don't know the exact rule but since "while" is used as a conjunction then there's no use for a comma in this case. If "while" was left out then I'd put in a comma so it read: "I am strong, my brother is weak."
English tends to "omit" commas in places where, I guess, most of the languages would require a pause. I always have problems with commas in English. If I don't know whether I should put a comma or not I prefer omitting it. It is safer way to be correct