Which would hit the ground first if dropped from the same height in a vacuum, a paper weight or a rock? Would the result be different on the moon?

This is the famous Galileo experiment of dropping two objects of different weight off a tower and seeing which hits the ground first. Consider this:

According to Newton, F = ma. The F (force) that is operating when you drop something is equal to its weight, so

F = W = ma.

An object's weight is its mass times g, the acceleration due to gravity. So

W = mg

and hence

W = mg = ma

Cancelling the m's:

a = g.

In other words, ALL objects fall with the same acceleration 'a' regardless of their mass. And that acceleration is equal to the acceleration due to gravity.

Now, can you answer what would happen on the moon, where the local value of 'g' is somewhat different? Clearly obhjects fall slower there (as you can see if yuo've ever seen any of the old videos of the Apollo moon landings). But do ALL objects fall at that reduced acceleration?

As far as my limited understanding goes, they would hit the ground at the same time, both here and on the moon.
The only difference would be wind resistance, negated by the vacuum, as on the moon.