Causation probably runs both ways on this one. There is a lot of evidence that richer and more-respected people are happier and healthier. Various explanations have been tried to explain this, including the explanation that health causes career success.

What about a third factor being the crucial decider in both, such the ability to handle/minimize stress levels? As you rise nearer to the top, stress increases. Those most able to adapt to it continue to rise, because high stress levels have a negative effect on brain function, and eventually the people who can't handle the stress are forced to fold. Stress also weakens the immune system and has other negative effects on health.

Logically it should hold that being able to effectively decrease stress would maximize both your chance to rise to the top and your health.