There are several theories of why this is true. Although why is less important than the fact that it is.

 Article - Science Daily

 Article - Live Science

     Not only do those who eat less live longer, but they are generally healthier. Add to that the time you spend working for the money to buy food, the time you spend shopping for food, the time you spend cooking, actual eating time plus elimination. Now think of how the quality of your life would increase if you cut out half of that. And we haven't even gotten to the chickens yet. 

       In 1912 Alexis Carrel placed a part of chicken's embryo heart in fresh nutrient medium, in a stoppered Pyrex flask of his design. Every 48 hours the tissue doubled in size and was transferred to a new flask. The tissue was still growing 20 years later, longer than a chicken's normal lifespan. After 34 years the experiment was cancelled with the conclusion that they could be kept alive indefenitely. "The cell is immortal. It is merely the fluid in which it floats which degenerates. Renew this fluid at intervals, give the cell something on which to feed and, so far as we know, the pulsation of life may go on forever..."   Humans live or die on a cellular level. When enough individual cells die, they call it organ failure. What kills the cells? Toxins from both outside and inside the body. Less food means introducing fewer toxins and, less waste produced by the cells themselves.

     I hadn't planned to put all this in the intro, but I guess that saves me from having to do a longevity page. Eat to live, don't live to eat.