How does weight depend on mountain altitude?

Using elementary mechanics and simplified models, this paper studies how the weight of an object varies with mountain altitude. After a brief discussion of the role of centrifugal forces, the effects of the mass of the mountain above and below the reference point are discussed and calculated, as well as the effects of the Earth’s curvature. The mountain shape factor is defined and calculated as a function of an appropriate shape parameter for a few cases of regular geometric solids. We discuss the theoretical conditions under which the weight could
increase with increasing mountain elevation.