The math shows that we would be weightless near the mass center of Earth. The moon and Sun gravity make hardly any difference as Earth is accellerated in the direction of their pull, mostly cancelling the slight gravity. We have not traveled even 1% of the way to the center. A slight increase (on the average) has been observed, thought to be because the average density increases with depth. The pressure is thought to be enormous due to the weight of the rock etc above. Neil