In the U.S. the only requirement is to hold a First Class FAA medical. Other than that the company doesn't not look into or have access to your current or historic health records. All they know is that you have that little certificate and there are no other health requirements.

Talking to some older pilots in the past there used to be a max weight requirement for some jobs. i.e. you had to be under 200lbs because you were flying a small aircraft where every pound counted. I don't know if any of those exist anymore.