Imagine a sphere of uniform density with similar volume and average density of our Earth. There is a bore leading to the center of the sphere from the surface with a scale at regular intervals. At what part of your journey towards the center would the scale read your greatest weight?
There are some caveats to consider. The sphere is in a very isolated region of space and has no angular motion.
I wrote this question down last night while I was having trouble sleeping. My intuition tells me that the surface of the sphere will have the greatest force of gravity. Any distance beyond the surface and the mass of the sphere above you will be reducing your weight. Is this correct?
If however the core is much more massive similar to Earth, one would feel a greater strain to stand upright as they descend.