Ya gotta prepare the child for the road, not the road for the child. You can't change every little thing that might cause a kid embarrassment. What happens when he feels his 40 jeans aren't good enough and he needs 100 dollar jeans so he won't be embarrassed? What happens when his new brother is born autistic and that embarrasses him? Institutionalize the brother so bumblebee isn't humiliated? What if his older sister has bad acne? Do we put her on accutane so precious doesn't have to go to school with his head hung down in shame? What if dad is terribly ugly? Do we put a bag over his head or make him get plastic surgery so junior can be proud to be in the family? And how about Grandma with the buck teeth? Send that old lady to the dentist so the little darling can feel good about his family. Good grief.

All those things would be as ridiculous as mom losing weight just to appease a kid who really, really needs to learn some manners and discipline.
If I were the parent of this child, I would use this as a great opportunity for teaching the child some life lessons. The mother doesn't need to lose weight if she doesn't want to. She needs to teach the child to be thicker skinned if people are in fact picking on him (which I doubt since more than half of his peers also have fat mommies). She needs to teach him the importance of family and always, always, always supporting the people he loves and who love him. He needs to learn that words hurt other people as much as they hurt himself. Lots of opportunity here to educate the child and make him a better person.