I hate to be so harsh, but it’s important to say. If you are a public figure for an organization where fitness is very important to success, you shouldn’t be fat.
I don’t necessarily need to say anymore, but just to be clear:
Your boss likely already thinks you are a “soft skill” or “leaf eater.” Don’t encourage this idea by being dumpy and out of shape.
Can you imagine doing a press conference while fat? It happens. Related: part of your organization’s internal and external message is that fitness is important and the organization is fit to fight. You’d be somewhat of an oxymoron.