A few years ago, West Virginia, which has the highest obesity rate in the nation, quietly began a small and unusual pilot program that would touch hundreds of lives: It started covering obesity drugs for state employees—even as many other insurers balked at what they considered expensive “vanity” drugs. The program was, by health measures, a success. Patients shed as much as 120 pounds, their cholesterol dropped, their prediabetes faded, and they cut down on blood-pressure meds. As word began to spread, more patients wanted to join. A school nurse told me her weight loss inspired at least six other...