In general, when there’s something helpful but socially awkward to say, SAY IT.
Example:
When I worked in a large corporation in a warm country, the person whose opinion I valued most was the one who felt least constrained by social politeness. She’s the one who’d tell me honestly if my work was shabby or if my personal hygiene needed…errr… “tweaking”.
Another example:
Until my childhood dentist said “you’ve got more cavities than the rest of my patients”, a seemingly rude comparison, I never realized that I had more cavities than normal. Until then I’d assumed that the treatments and coaching I was getting was something that every kid heard, regardless of how well they brushed & flossed.
Honesty improves objectivity. Objectivity gives people the facts and impetus they need to do necessary things.
It’s even possible that you’ll hear a reply from “fat guy” that increases YOUR objectivity. For example, he may say that he can’t exercise / has a glandular condition or heart condition / etc. that prevent him from bringing his weight within normal range.