Answer:
The force of gravity between an object of mass m and Earth M at distance r is as follows (G is gravitational constant):
F = (G) x (m) x (M) / (r^2)
Now, we also know that a force acting on the object is F = (mass) x (acceleration).
Rewrite the first formula as:
F = (m) x (G x M / r^2)
The (G x M / r^2) part is precomputed for the near-surface of Earth and is referred to a gravitational acceleration g:
F = (m) x (g)
As you can see g (or G x M / r^2) does not depend on the mass of the object, only on the mass of Earth but that is the same for all objects in free fall (towards Earth).
