Idea
Here's a thought:
Maybe, slim people only develop these diseases if they are naturally "weak"
i.e, 10% of the normal population develop Type 2 diabeetus, while 80% of the obese population do.
Now, the diabeetus might be more lethal to the slim people, because they developed it through natural fallibility, however, that doesn't mean that the obese population is more healthy than the normal population.
Let's say that it kills 80% of the normal population who develop it, and 30% of the obese population. That still means that 8% of normal people develop lethal diabeetus, while 24% of the obese do.
Thus, this disease is more lethal to normal people who develop it, yet overall kills a greater percentage of the obese population.
These numbers are, of course, just an example. I'd have to see the data from the actual studies to make an informed judgement.