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Weight varies as the distance from the center of the earth varies.
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since acceleration due to gravity varies, so does weight. weight decreases as you move away from centre of earth
At the centre of Earth you would be weightless, since the forces acting in all directions would cancel out.
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At the exact center of mass of the Earth you would be weightless. This is because all of the mass around you cancels each other out. For this same reason as you drive through a tunnel in a mountain you weigh less. The mass of the mountain above you attracts your mass.
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