You would think that obesity and malnutrition were direct opposites. Not true, at least not in Britain. According to an article in the Seattle Post Intelligencer:

There are no statistics on how many obese people may be malnourished, but doctors say they are seeing patients who are both overweight and malnourished.

The article goes on to explain:

While malnourished fat people are hardly in danger of starvation, other health problems are possible along with obesity-related complications like diabetes and heart disease. Once they start losing weight, malnourished people may actually burn their own tissue, including muscle, rather than fat.

From the London Daly Mail:

....... our growing reliance on fast food, coupled with soaring rates of binge-drinking, means many are lacking the vitamins and minerals essential for health.

The result, in the most extreme cases, is pot-bellies, wasted limbs and emaciated bodies - all conditions more usually associated with famine victims in the developing world.