This is a great question because it introduces so many interesting things. But where to start ...
Let's start with Newton and his universal law of gravity. This says that the gravitational pull (force) between two objects, for example the earth and your stone, depends on three things: the mass of the two objects and the distance between them.
Mathematically, this is:
Where
M is the mass of the Earth (in this case),
m is the mass of your stone (or leaf),
r is the radius of the Earth,
f is the force on the object and
G is just some constant that relates all these.
What this shows is that the "pull" on an object on Earth is just dependent on its mass. And, on Earth, this pull is what we call weight. So a big stone weighs more (has more gravitational pull) than a small one or a leaf.
If you went to the Moon, that same stone would weigh a lot less because M for the moon is much less (and the r is smaller too).
Now for the really neat bit. When you drop your stone it accelerates towards the ground. The rate at which it accelerates is determined by two things: the pull (force) and the mass of the stone. In other words:
.
What this means is that a larger stone has a stronger gravitational pull BUT it accelerates more slowly because it is more massive. This exactly cancels out so that all weights fall to earth at the same speed (as demonstrated by Galileo dropping things from the leaning tower of Pisa).
Finally, we get to the leaf versus stone thing. This is where surface area comes in. A leaf falls more slowly (and drifts around) because of air resistance. On the moon (no air) the leaf and the stone would fall at exactly the same rate (but slower than on Earth). You can find videos online of astronauts on the moon dropping a feather and a hammer to show they fall at the same rate.
Hope that helps (and I really hope it wasn't a homework question!
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