You are all raising some great points! I'm not sure I have any insight into the paradox, but I’ll take a stab at it.
The answer may well be this: being overweight is bad for some people but okay for others. The problem is we haven’t fully identified the people in each group.
I always tell my students that if you want to sound savvy about research, one good question to ask about studies is: "How did they measure that?" In this case BMI is the answer (for one of the variables), and may not be the best measure at all (as Amy and LaurieDawn suggest)! What if they tried to use something like body fat percent? It may shed some light on the results!
The second question to ask is: “Who did they study?" You may find, for instance, that the population studied is a group of males over 50 with cancer. Do the results then apply to other populations? Who knows?
In this case, what if they have never really looked at people with certain kinds of habits (exercisers for instance). Maybe if you exercise regularly, being overweight is less of a problem than if you do not.
Sometimes if you start investigating the populations and the methods the research turns out to be less contradictory than it first appeared to be. The problem is, all of that takes time, and we want answers now!
But a big problem IS the media. Science never professes to answer any question with a single studies, or even a few. But the media frequently makes it sound like every study is definitive. NO single study is definitive. Ever.
But that doesn’t mean we don’t know anything, or we never learn anything. I think if we take a step back, we can often see a big picture emerging. For instance, I recently read an article in Scientific American which suggested that, despite all the fads out there, the overall guidelines for a healthy lifestyle haven’t changed a whole lot in 50 years: eat lots of fruits, veggies, lean protein, and whole grains (remember the whole “oatmeal is amazing” trend a number of years back?) – and get regular exercise. Lots of research back up those claims and do continue to find benefits of these behaviors.