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The weight of an object would decrease as you go towards the centre of the earth, since the force of gravity decreases with depth and weight is mass x g. It would eventually become zero in theory. The mass of an object would stay the same in theory.

Another way of looking at the question is considering density, this increases with depth to huge amounts at the core. The mass of a given amount of material would remain the same, but the pressure would crush it into a smaller space, increasing the density.

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Q: Do the materials toward the earths center have less mass than those on the surface?
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