* Weight vs. Mass: Weight is the force of gravity acting on an object's mass. Mass is the amount of matter in an object.
* Gravity's Influence: While gravity does slightly decrease as you move further away from the Earth's center, the difference in elevation between sea level and the deepest valley (the Challenger Deep in the Mariana Trench, at about 11 kilometers deep) is insignificant in terms of gravitational change.
* Negligible Change: The change in weight would be so minuscule that it wouldn't be noticeable. Even at the top of Mount Everest, the highest point on Earth, the weight of an object would only be about 0.3% less than at sea level.
In conclusion: The weight of an object would remain practically the same whether it was at sea level or in the deepest valley on Earth.