The study also found some obese people are no more likely to get cancer than normal weight people.
Another study finds, for patients with heart disease, being obese may actually reduce the risk of death.
Both of these reports are published in the online journal European Heart Health.
But, experts are quick to add, relatively few people fit this category.
One critic says, sure, it is possible to be fit and fat or thin and unhealthy, which is why health, not a particular weight , is what most people should be aiming for.