Newton's second law states that F=ma, where F is the net force, m is the mass of the object, and a is the object's acceleration. For free-fall and projectile motion, a = gravitational force. In general, the gravitational force is defined as Earth's inward gravitational pull (a = 9.81m/s^2). The gravitational force is always the same for all objects on or near Earth's surface, so changing the mass will only change the net force; it has no impact on gravitational force.
However, the distance between an object and Earth's surface affects gravitational force. On the surface, all objects experience a downward pull of -9.81m/s^2, but as the object moves farther and farther away from Earth, the gravitational force decreases. This is reflected in Newton's Law of Universal Gravitation, where the attractive forces between two objects decrease as they are farther apart.
