Question

Explain why the gravitational acceleration of any object near Earth is the same no matter what the mass of the object is.

Answer 1

-- It takes more force to accelerate a larger mass with the same acceleration
as a smaller mass accelerates from less force.  They're directly proportional.
(Newton's second law of motion.  Can never be proven.  "Just a theory."  But
no exceptions have been observed, and it makes predictions that are always
true when we test them, so it's accepted as a law.)

-- But gravity pulls on a larger mass with more force than it pulls on a smaller
mass.  Those are directly proportional too.
(Newton's law of universal gravitation. Can never be proven. "Just a theory."
But no exceptions have been observed, and it makes predictions that are always
true when we test them like the orbits of planets and satellites, and the things we
build that need it to work like space probes and TV satellites always work, so it's
accepted as a law.)

So it all balances out.

-- Gravity pulls more mass with more force, and less mass with less force.

-- The larger force pulling the larger mass, and the smaller force pulling the
smaller mass, accelerate both masses at the same rate.

Neat, eh ?  Jever wonder who set it all up to work like that ?