Muhammad Al-Hakeem asked:
As we progress down to the very centre of the core of the Earth, why does gravity weakens while gravity should increase toward an object? And why does pressure take over?
There is a similar discussion here.
Perhaps one could consider the gravity at the center of the Earth like standing at the North Pole.
It is a common mistake to think that because the text books say that the surface gravity of an object is as if all the mass was concentrated at the "centre of gravity" of that object i.e. the centre of a spherical object they fail to stress that the gravity falls off linearly to zero as you approach the centre of the sphere.