As you descended inside the earth, you would weigh less because there is mass above you which also pulls on you. In fact, mass above your depth cancels out the mass on the opposite side, and in the end it is only the mass interior to you which gives you weight.

Deeper down, your weight would become lower and lower until at the center of the earth, you would float since earth's mass all around you would tug evenly.

So the place to experience an object's strongest gravity is on its surface. No wonder you would weigh a trillion pounds if you stood on a neutron star! It's as compact as material can get and still be in the universe!