Do heavy things fall faster than small things?

In a vacuum (ie in the absence of air resistance) all things fall with exactly the same acceleration. The reason for this can be easily seen.

An object, with mass ‘m’, falling in a gravitational field in a vacuum experiences only one force F. Newton tells this force is given by:

F = GMm/r^2

The consequent acceleration is given by Newton's second law:

F = ma

Notice that both equations contain the mass of the particle 'm' even though the 'm' is playing completely different roles. In the first equation it is telling us the force a particle experiences for a given gravitational field, in other words how susceptible a particle is to a gravitational field (the gravitational mass). In the second it is telling us how difficult (or easy) it is to accelerate the particle with a force, that is, how much inertia it has (the inertial mass). If we didn't know anything about the universe we would assume that the inertia of a particle and its susceptibility to a gravitational field were completely unrelated and therefore that the gravitational and inertial masses were different. It is therefore an interesting fact about the universe, which was first discovered by Galileo (although he didn't know about Newton's laws), that these two masses are actually the same and so we simply talk about one mass 'm'.

As a result when we equate the two equations the mass cancels and we get:

a = GM/r^2, which shows that the acceleration of a particle depends only on the mass of the object causing the gravitational field, M, and the distance, r.