Just to elaborate a bit, if you think of a hollow earth then inside the hollow there is no resultant gravitational force and you would be weightless.
So if you think of a point inside the hollow, then as the hollow part gets smaller and smaller the point still experiences no resultant force, and so when the point is at the centre of the sphere then again there is no resultant force.
All this assumes that the earth is a perfect sphere and that the mass density is constant for any given shell; put another way the mass density only varies with distance from the centre.