If I understand my Physics 103 class correctly, then answer is technically yes. We measure gravitic pull from the center of the particular mass, outwards. The further you are from the center of the Earth, the less of an effect Earth's gravity has on you. So technically, yes, you would weigh a teeny, tiny, itty-bit less on top of Mt. Everest than at sea level. Also, time would move somewhat faster at the top, than at sea level.Remember Newton's Law of Gravitation? F=G.M.m.(r^-2). The force between two bodies is inverse-square proportional to the distance between them. At the top of Mt. Everest, one's center-of-mass is several thousand feet further away from the center-of-mass of the Earth than at sea level.
On top of Everest you will weigh slighly more because of the increased mass (caused by the mass of Mt. Everest) pulling against you.
Of course that's just speculation on my part and I really don't know squat.