If, say you had a bubble in the middle of the earth, then there would be no gravity in the bubble (i.e. one would simply float in the bubble like in space). That may not be exactly true because the gravitational center of the Earth shifts somewhat because of the moon, sun, and other celestial bodies, but it is close enough.

However, say you measured the pressure/weight contribution of all the rock, say 1 mile from the center, it would also have a negligible contribution to the pressure at the center. But, if you add up the mass of the rocks for 3,959 miles (6,371 km) in any direction from the center of the Earth, the total contribution of weight of the entire column (or wedge) of rock would be extreme. Thus you get pressed from all directions by the high pressure.

Now, there is a bit of a static vs dynamic pressure paradigm, but not real exciting. Say you hold a walnut in your hand. Now place a 5 pound anvil on top of the walnut. You press up with 5 pounds, the anvil presses down with 5 pounds. It is the same if you place it on the table. The anvil presses down with 5 lbs, and the table presses up with 5 lbs. So, how many Pounds of pressure does the walnut experience? Well, it is 5 lbs, not 10. Perhaps it would be best to consider the pressure per square inch on the walnut. If each half of the shell is about 1 square inch, then assuming even distribution of weight, it gets 5 psi on top, and 5 psi on the bottom. Sum it, and one gets 10 lbs over 2 sq in, or 5 psi overall.