CHICAGO—You can look great in a swimsuit and still be a heart attack waiting to happen. And you can also be overweight and otherwise healthy. A new study suggests that a surprising number of overweight people—about half—have normal blood pressure and cholesterol levels, while an equally startling number of trim people suffer from some of the ills associated with obesity.

The first national estimate of its kind bolsters the argument that you can be hefty but still healthy, or at least healthier than has been believed.

The results also show that stereotypes about body size can be misleading, and that even “less voluptuous” people can have risk factors commonly associated with obesity, said study author MaryFran Sowers, a University of Michigan obesity researcher.

“We’re really talking about taking a look with a very different lens” at weight and health risks, Sowers said.

In the study, about 51 percent of overweight adults, or roughly 36 million people nationwide, had mostly normal levels of blood pressure, cholesterol, blood fats called triglycerides and blood sugar.