simple experiment to confirm this. Drop two objects with different masses (like a cat and a llama) inside of a vacuum (so there is no air resistance) and you will see that they fall at the same speed. Why does that happen? If the gravitational mass of the llama is larger, then it gets pulled by a larger force from the Earth; but since the llama also has a larger inertial mass, it takes a larger force to get it moving. The two effects perfectly cancel out each other, and the cat and llama fall at the same speed.
