The more sugar you eat, the more AGEs you develop. As AGEs accumulate they damage adjacent protiens in a domino-like fashion. The most vulnerable protein harmed by AGEs is collagen and elastin. These are two protein fibers that keep your skin firm and elastic. In fact, collagen is the most prevalent protein in your body. Once AGEs damage collagen, they become brittle, sagging, dry and start the process of premature aging.
The damage from a high sugar diet starts for most adults around the age of 35 and increase rapidly after that. This is one of the many reasons getting older really sucks, we just cannot eat the things we want to.
These studies on sugar and skin damage have been published in the British Journal of Dermatology.