(CBSNEWS) — Despite all the obesity studies and news reports on how unhealthy eating and inactivity are recipes for chronic disease or worse, a new survey finds Americans aren’t getting the entire message.

The survey found that many Americans know about heart disease and diabetes as major health risks from obesity, but few realize other conditions including cancer, arthritis, sleep apnea and infertility are tied to having excess weight.

Only about one-quarter of people think it’s possible for someone to be very overweight and still healthy, according to the poll by The Associated Press-NORC Center for Public Affairs Research.

When asked about the most serious consequences, more than 7 in 10 Americans can correctly tick off heart disease and diabetes. Heart disease is the nation’s leading killer, and diabetes and obesity are twin epidemics, as rates of both have climbed in recent years.

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