At the moment, I wouldn't worry about his weight. That sounds like it is probably as a result of his depression. What you might want to do is a little research before you approach your son again. See if they have counseling through the college. A lot of schools do. Also find a private therapist or counselor who is skilled with young people and their problems. Then offer your son his choice.

Tell him that sulking and hiding at home is no longer an option. There is no shame in grief or depression, but it also cannot be allowed to continue forever. Offer to drive him to his first appointment or he can go alone, but tell him you want him to go for at least two sessions. You will pay for it.

If he doesn't like the town he lives in then he can start actively investigating some sort of internship program that will take him out of town for part of the summer.There are plenty of service/internship programs for students.

Inactivity begets more inactivity. I wish you and your son the very best.