Then what of the famous formula e = mc^2 ? (I'm not sure if this is sarcasm)

This formula basically means energy is mass. Energy is potential to do work.

What this means is that its much like charge in a capacitor, or power in a battery.

The statement that falling objects cannot be measured for weight is accurate because all objects in the gravity's pull fall at the same rate (Galileo Galilei falling bodies experiment).

What this means is that gravity is not a result of masses, but an effect which affects masses and masses are affected in different ways depending on their status, like if they are at rest or falling or spinning (see rifling). Masses can also affect gravity.

I will do my best to explain my knowledge of gravity, to make better sense of the phenomenon.

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Geometry of the gravitational field = mass density affected

Spacetime is a mathematical extrapolation of a higher dimension. In the higher dimensional perspective, a lot of things which seem nonsensical to us make perfect sense. This is pretty well described in Carl Sagan's video about the dimensions, which helps explain it in laymans terms;

youtube.com/watch?v=rAAeLNAfSYc

To the best of my knowledge these higher dimensions are fractal and so can be rougly figured out using the 3rd dimension as a sort of a reference. The 4th, 5th and 6th are temporal, given what I've studied.

As for curvature, this is referring to higher dimensional geometry. It may be time variant, in motion and doing complicated things. The gravitational field may be described as an interplay of substance with higher dimensional elements.

The geometry is that of a higher dimensional vortex. To us it may look like a hole from any angle, but in a higher dimension this makes sense.

The interesting part is that since the geometry of the gravitational field can be affected by masses/energies, it can be distorted in such ways as to affect gravity.