Will using the Stairmaster make my legs and rear-end larger?

That extra stuff around your rear is not something that keeps growing from exercise; it’s from eating too much. Don’t worry about any exercise making your rear bigger; you couldn’t even measure the difference. Just keep moving, eat less and watch it shrink. If the exercise is done at the appropriate intensity to make it aerobic, the stimulus will not be sufficient to cause muscle hypertrophy (growth). Often what happens is that when one begins an exercise program, their hunger may increase or they may begin justifying additional food (the "I earned this" syndrome). If caloric intake exceeds expenditure, then fat stores can increase. This may occur on the thighs and buttocks but not from exercise.  It's from a calorie imbalance.