These two monkeys were part of a decades long experiment. Monkeys were divided into two groups. Both groups were fed exactly the same food (albeit high in sugar to mimic a modern western diet).
One group had food freely available. The other group had their food restricted to a daily amount that maintained a healthy body weight.
The pictured monkeys are close to the same age, but as you can see one is decrepit and the other looks healthy. It's not only looks that matter check the differences in their brains.
The white part is the healthy brain matter, and the"white" brain belongs to the restricted intake Monkey.
So in answer to question, just eating healthy food doesn't mean we won't overeat, and if we overeat we will be shortening our health span relative to what it might have been. You can read the details of the experiment HERE.
Humans are different to monkeys, you can find out why HERE