A TV documentary in 2002 said they studied 2 groups of rats. The control group had a steady supply of food and could eat whenever they want. The other group was on a diet.
After 2 years, the control group all sat in a corner of their cage being fat and lazy. The other group continued powering their ferris wheel generators and were not being lazy at all.
They hypothesized that too much food made the body more prone to free radicals and the damage was more difficult to repair in the control group. Effectively making them age faster than the diet group.