First define the question clearly.
In free fall, mass has no effect on the acceleration of a falling object. The speed is related to the amount of time the object has been falling.
In situations where there is air resistance, the shape (surface area) and speed of the object affect air resistance. How this affects acceleration (and ultimately the terminal velocity) of the falling object does depend to some extent on the mass. Acceleration will be determined by the net force which will be the weight of the object (proportional to the mass) minus any resistance forces. It would be expected the resistance forces increase until they equal the object's weight. At this point, velocity remains constant.