Lesa Walton suffered for years with rheumatoid arthritis. “It was awful,” said Ms. Walton, 57, who lives in Wenatchee, Wash. “I kept getting sicker and sicker.”

She also had high blood pressure, and she was obese. Doctors told her to diet and exercise, which she did, to no avail.

Then she found a doctor who prescribed Wegovy, one of the new obesity drugs. Not only did she lose more than 50 pounds, she said; her arthritis cleared up, and she no longer needed pills to lower her blood pressure.

Her new doctor, Dr. Stefie Deeds, an internist and obesity medicine specialist in private practice in Seattle, said that Ms. Walton exemplifies a growing movement in obesity medicine.

Proponents call it “obesity first.” The idea is to treat obesity with medications approved for that use. As obesity comes under control, they note, the patient’s other chronic diseases tend to improve or go away.

“We are treating the medical condition of obesity and its related complications at the same time,” Dr. Deeds said.