To Paul Williams, spurring more exercise out of the half of Americans who are already active is just as important as coaxing the sedentary off the sofa.

In Dr. Williams' study of more than 100,000 runners over nearly 20 years, stepped up exercise was found to have some powerful benefits. But his research is controversial. While Dr. Williams is well respected by other exercise scientists, he is shunned by those in the public-health field. Dr. Williams is routinely excluded from committees charged with formulating exercise...