This Parker being overweight thing is ridiculous. Whether or not he has 4% body fat or 9% isnt going to make much of a difference. The dude is going to ball regardless. Some guys dont need to be shredded to be ballers.
I think his future team would at least like to see him lose weight once during his rookie contract to find out if a lighter version can succeed better on the wings and if he's still slow you simply make him regain the weight in strength. With his rookie contract he'll hire a personal cook if he listens to advisors.
I think Jabari struggles with weight a little vs. doesn't struggle.
I think I'd be more concerned with work ethic than weight. (not because he's lazy)
Question is if his weight is an result of food preferences and selection. That's also part of work ethic btw. What I said in my first comment should also apply to this as a personal cook will serve him new dishes that maybe can serve the same roles that high calory sweets did in the past.
Sidenote: I'm in no way ruling out that he's chubby as a result of a disfunctional metabolism.