i agree with agnurse, et alia.
your comment about feeling embarrassed to be seen with him is very revealing. this attitude is probably obvious to your SD, and may remind her of her own mother's unhelpful approach. she is exercising great patience and self-control not to say something dismissive to you. probably out of respect for her father.
if you really think it as endangering the boy, report it to social services, anonymously.
but really it is not your place to get involved unless asked.
and to suggest a child go to a slimming club, or even worse a fat camp as per pp, well, no wonder youngsters have self-image problems. leave them alone, esp as you find it embarrassing.
to the people above who say the mother controls what he eats, that is not realistic. this is not a toddler. he can open cupboards, fridge, to graze, as 90% of the adult population do, esp when at home on lockdown.