When an object made of paper is fired using a rubber band the initial velocity of the object is dependent on the mass of the object. If it is assumed that when the object is shot the rubber band is pulled back by the same distance and released, the potential energy stored in the rubber band that is transferred to the paper object is the same. This potential energy when converted to kinetic energy gives a heavier paper object a lower speed than is the speed given to a lighter object. The acceleration due to gravity is the same for all the objects.
Also, paper objects of different sizes face different levels of air resistance. This changes the force opposing their movement and the resulting acceleration due to the force of air resistance.