Obesity Paradox
The Obesity Paradox is a relatively recent invention. 100 years ago it was considered healthy and actually was healthy to be obese. Obesity gave a survival advantage in the diseases of the time as well as resistance to famine. This is why I was hounded by my elders to "put some meat on my bones". They lived through the obesity advantage.
The modern obesity paradox is most likely due to the fact that a skinny chronically ill person is worse off than their overweight counterpart. Therefore they have less "reserve capacity" in case of acute illness.
When one looks at healthy thin people vs healthy overweight and obese people nowadays, the thin do have an advantage. This is because obesity itself is a chronic illness and leads to many other acute and chronic diseases in our modern, well fed, TB free (hope it stays that way), and information oriented society.
A skinny farmer can't work the fields by hand all day. A thin construction worker who worked without safety equipment had a much greater chance of getting killed than a hefty counterpart. Today a fat desk worker is more likely to plug an artery in the heart than the skinny counterpart.
In the same way a skinny diabetic who develops influenza or pneumonia stands a better chance of dying due to a lack of reserve nutrients and strength. I know that the research authors "adjusted" for level of illness but my intuition tells me otherwise. Medical statistical analysis is a very inexact science.