A talmid chacham once told me that whatever time you invest from learning when you are young to keep yourself in shape and thin, will pay off in more learning time when you are old, since your body will be healthier, and you will need to spend less time at doctors. While we can’t ever be sure of that, as only the RBSH knows, it seems to make sense. We must take care of our bodies, and not let them go to pot.
One also sleeps deeper, and may end up needing less sleep to feel rested, when in shape. After a long run during the day, one simply collapses into bed that night and wakes up refreshed the next morning.