The "overweight" category is to the obesity panic what marijuana use is to the drug war: stories about an "epidemic" of fatness depend crucially on classifying the 35% of the population that's "overweight" as being at some sort of increased health risk. This is simply false, and is known to be false by the researchers who are quoted in stories like the one linked above.
But the situation is much more egregious than even this suggests. Note that the NHANES III data reveals that most people who are classified as obese have a lower mortality risk than so-called normal weight people. About two-thirds of "obese" Americans have a BMI of between 30-34.9, and currently we're seeing about 14,000 fewer deaths per year in this group than would be expected if the group's mortality risk was the same as that of "normal weight" individuals.
This subject always interests me. As a person who struggles to reach and stay in that "normal weight" category, I can tell you that there are many problems with the idea that thinner=healthier. All of the things that are supposed to scare people into wanting to be thin (e.g. cancer, heart problems, early death) won't be prevented just by losing weight. You can still die, you can still get cancer, you can still develop heart problems, no matter how much you weigh. Whether you will face these issues is not just determined by your weight. It's much more complicated than that. There are genetic tendencies that play a much greater role in this than weight does for most people.