Falling objects

Why do objects of different masses dropped from the same height always fall at the same velocity, and experience the same acceleration? I have some vauge idea, but I'm not entirely sure.

Larger masses have a greater force on them, so you'd expect them to fall faster.

My physics teacher couldn't really explain this without showing me two formulas, equating them, and then cancelling out the "m"s. I'd rather have an explaination that gives me an understanding of what's going on.

Oh yeah, neglect air resistance.

This is boring, >>1 obviously just wants an explanation of the terms. >>8 got it right, and >>11 is a dipshit who doesn't really understand what he's saying despite being partially right as well (gravity is quite mysterious by nature, but its effects aren't).

>>1
The formulae are not circular. Let's just take a look at each formul and see what it's saying.

The force pulling the object down towards the earth is its weight
P = m g
where P is the force, m is the objects mass, and g is the "gravitational pull" of the earth. So far, so good. (if not, see note at the end).

But remember, according to Newton's second law, F = m a, where F is the force, m is the mass of the object, and a is the acceleration the force causes on the object. This just goes to show that for objects of different mass, you need to apply more force on the more massive one to produce an equal acceleration.
a = F/m so if m1 > m2, to have F1/m1 - F2/m2 you need F1 < F2 (more specifically F2/F1 = m1/m2). So hopefully your get the whole, F = ma thing.

In the case of weight, F = P.
In short, we can write that the acceleration due to the earth's gravitational pull is equal to a = P / m
so a = (m g) / m
thus a = g (kinda predictable).
g being fairly constant over a small area, and not varying that much over the surface of the globe, aside from the effect of friction objects will fall with the same acceleration and therefore obtain similar velocities simultaneously.

The only thing that can cause objects to fall at different speeds is change in g (for example if I drop a ball in the north pole, and you drop it in North Africa...)