Ordinarily, of course, your legs have hair. Beneath the skin, hair follicles are kept alive by the blood flowing through your veins and arteries. When you gain weight, over time your cholesterol level rises and plaque builds up in arteries, clogging them up and cutting off blood flow. As a result, all the little blood vessels under the skin die off, killing hair follicles. If you notice shiny, hairless skin around your feet, it may indicate plaque buildup, which could eventually lead to a deadly heart condition.
The good news is, you can often stop or even reverse the buildup of plaque in your arteries with proper diet and exercise. Be sure to consult with your doctor.