Actually, at the very center of the Earth, in theory, if it were indeed possible to go to such place, there would be no gravity!
Why? Because at the very center, all of Earth's mass is causing gravity at all directions and would thus 'cancel' each other out and be zero gravity. It is still causing gravity, its just that the force is equalibrium here.
Let's say at the North Pole someone dropped a ball, and at the same time someone else dropped another ball. They are both falling to the ground but because on opposite sides they are actually falling 'towards' each other. Somehwere in the middle these two gravity forces in opposite directions must equate out to zero.
However of course, the pressure and temperature in the centre would be beyond extreme. The Earth's core is liquid molten iron, and the heat is maintained by the pressure caused by both gravity pressure as well as stress on the physical planet by tidal forces from sources like our moon, and perhaps a lot of the heat from Earth's formation is being partly preserved down there. It is very gradually cooling, though.
These tidal forces account not only for the molten state of Inner Earth, but this in turn leads to the convection currents and the tectonic activity that occurs to Earths crust. The iron core also causes Earth's magnetic field, and these convections may also account for why Earth's magnetic field subtlely changes over time, and has even swapped around completely a few times.
Back to what you were saying, gravity would not actually be greater if you were inside Earths center, but the mass and density of the matter down there compounds on the gravitational pull closer to the crust. Gravity is caused by Earths layers right up to the crust, though the crust is of different density (I think lighter despite being solid rock) and compounds less gravity to whats below.
So in places where the crust is thickest (e.g around India near Himalayas) gravity is ever so slightly lighter (can't remember for sure now), but the difference is too small to physically notice.
No chance of Earth being hollow, this is most likely the densest place of all!