In the case of falling objects, at a point during motion, the air resistance acting on the body equals the weight of the object. From that point the object will move with a constant velocity; called terminal velocity. That is the acceleration of object is zero.
As massive bodies will have higher terminal velocity as compared to lighter objects, they faster than lighter object. It implies that heavier object has more mass and hence more gravity acts on it. So, more air resistance force required to achieve terminal velocity (to slowdown). So, heavier objects move faster as compered to lighter ones.
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