I was watching a program about the geoid recently and the relative "height" of the Himalayan plateau gave me an idea. It makes sense for the geoid to be "highest" (is that the correct term?) there as there is more mass underneath you than in other places, however I remembered from physics that your distance from the center of the earth effects gravity as well.
So if you were on the peak of Mount Everest what would have a stronger impact on your weight as compared to say sea level at a comparable latitude (to control for the spin of the earth), there being more mass underneath you, or you being further from the center of the earth? In other words, would you feel slightly lighter or slightly heavier?
I tried working it out myself, but I haven't done any calculus in over fours years, so I couldn't figure it out.