So um, how do you know that acceleration due to gravity is slightly less atom Mt. Everest?
It could be that you went up there yourself and measured the miniscule difference using highly sensitive, delicate, complex, and expensive lab equipment that you brought with you.
Or, it could be that you are merely listening to the claims of people who went up there themselves and measured the miniscule difference using highly sensitive, delicate, complex, and expensive lab equipment that they brought with them.
Or -- and I predict that this is really what is going on here -- you or somebody else assumed that gravity on the Earth follows an inverse square law and computed the miniscule difference sitting comfortably at a warm desk someplace not too far from sea level.
Question well begged.