String Theory: A Matter of Mass
When you read that the force between objects is proportional to the mass of the two objects, you may think this means that heavier things fall faster than lighter things. For example, wouldn’t a bowling ball fall faster than a soccer ball?
In fact, as Galileo showed (though not with modern bowling and soccer balls) years before Newton was born, this isn’t the case. For centuries, most people had assumed that heavier objects fell faster than light objects. Newton was aware of Galileo’s results, which was why he was able to figure out how to define force the way he did.
By Newton’s explanation, it takes more force to move a heavier object. If you dropped a bowling ball and soccer ball off a building (which is not recommended), they would accelerate at the exact same rate (ignoring air resistance) — approximately 9.8 meters per second.
The force acting between the bowling ball and Earth would be higher than the force acting on the soccer ball, but because it takes more force to get the bowling ball moving, the actual rate of acceleration between the two is identical.
Realistically, if you performed the experiment there would be a slight difference. Because of air resistance, the lighter soccer ball would probably be slowed down if dropped from a high enough point, while the bowling ball would not. But a properly constructed experiment, in which air resistance is completely neutralized (such as in a vacuum), shows that the objects fall at the same rate, regardless of mass.