There may be several reasons why this might happen. The first is that the shoes you're wearing may not be right for you. They may be too small, too big, too loose, tied too tightly or not well-cushioned enough.
Another possibility—your physical position while using the equipment may be putting too much strain or pressure on certain parts of your leg or foot. Keeping your feet in a stationary position throughout the workout, and not moving them, creates constant pressure. As a result, your circulation is restricted—which leads to a numb or "falling asleep" feeling. Being 100 pounds overweight adds even more pressure to your feet.
Change your form slightly and see if there's a difference. For example, on the elliptical, try lifting your heels as you go through the motion, rather than keeping your feet completely flat on the pedals. Also, wiggle your toes at times during your workout to help with circulation.
You may want to shorten the amount of time you spend on the equipment. If you're doing 30 minutes in a continuous session, but your feet start to fall asleep at 15 minutes, then do two bouts of 15 minutes each (with a break in-between).
You could also have a circulatory or nerve problem. Consult your health care professional to have the problem checked out.