Originally Posted by KC Fish
Not exactly. It has a lot to do with the mass around you right where you are. More mass around you means more gravity. When you go further into the surface, theres less Earth below you to pull down. The farther you go, the less of Earth there is below pulling you down and the more Earth mass there is above pulling up. At the center you would be weightless because there would be equal mass above and below you, canceling each other out.
That reminds me of a question I heard/read somewhere:
If you could install a tube from one side of the earth to the other, somehow shielding it from the molten core and suck all the air out, what would happen if you jumped in one end?
The answer as explained was that you would go falling through the tube, accelerating quickly at first. You would slow down as you went through the center, but your inertia would carry you to almost the other of the tube, where you would come to a complete stop and get pulled back down. You would basically do this over and over and over, travelling a little less each time, until you were just floating in the center where the pull of the earth is the same in every direction (minus the directions of the empty tube).
I don't know if it's the correct answer, but it seems plausible and I've always wondered what it would feel like.