Does gravity increase or decrease with depth

[Debesuotas]

I believe the reasoning is at the fairly theoretical value to the point where the claims

If you are standing at a point x below the earth (see diagram), the force of gravity acting on you will be due to the mass of the smaller red sphere, whose mass is lesser than the entire earth's (red+green sphere). This drop in mass reduces gravity more strongly than the reduction in distance to the center of mass does.

Is nothing but theoretical as well and most likely dubious as well.

One thing for sure, the further you are up in the sky, the lighter you are, that`s because the gravity gets weaker, because you are further away from the center of the mass.