No. If an object is heavier the force of gravity is greater, but since it has greater mass the acceleration is the same, so it moves at the same speed (if we neglect air resistance). If we look at Newton's second law, F = ma. The force of gravity is F = mg, where m is the mass of the object and g is the acceleration due to gravity.
Equating, we have mg = ma. Therefore, a = g.
If there was no air resistance, a feather would fall at the same speed as an apple.