I've been trying to rationalize why my intuition tells me that fat reserves would be more susceptible to harbor pathogens, but so far all I could come up with was the fact that there is less blood flow to fatty areas, meaning less immunological helpers circulating throughout. So I'm not sure how likely it is that there may be a correlation there.
Anyway, I'd argue that the impact of obesity to health is still of much significance. Not for all people, naturally, but for many it can be a major deficiency when fighting illness. If important muscular organs become infused with too much fatty tissue then they must work harder, and thus less efficiently. That, and the fact that there is more tissue overall for the various fluids to circulate through means the metabolic rate may be much lower than normal. Also, substances that would be more readily expelled otherwise may linger in the fatty tissues (which really relates to my first point).
Also, I think the attribition of thinness, per se, to higher rates of illness is fairly unlikely. Obviously, if the person is malnourished, it will certainly be more difficult to fend of pathogens. But the same goes for obese persons who are malnourished (eg. too much junk food). I'm fairly thin and haven't gotten sick in years, and when I do I recover quickly. This wasn't always the case. When I was younger, my primary caretaker wasn't exactly the most concious about the importance of wholesome foods, ample water consumption, clean air, exercise, etc, and as a result, I think, I was much more vulnerable to disease/infection/fatigue. Fortunately, someone did finally step in and remedy the situation, and my vitality/health did increase dramatically. Point being, those factors are *much* more important than weight, by several orders of magnitude. Beyond that, the most essential tool for healing is the mind itself, which operates on many levels to produce conducive conditions for self-repair. That's overlooked way too often, I think.
So in short, a healthy lifestyle plus positive thinking generally ensures the best protection against illness, all things considered.