Question

what happens to acceleration due to gravity if you climb the tallest mountains on the earth ?

Answer 1

It decreases very very slightly. Mabye from 9.81m/s^2 to 9.80m/s^2, MABYE.

Depending on how far you travel away from Earth, the force due to gravity is decreases exponentially. This can be proven with Fg=Gm1m2/r^2 where G=Gravitational constant(6.67*10^-11 N*m^2/kg^2)