Using Einstein's geodesic equation, you can calculate the path of an object (that is, its motion) thru space as a function of time. The "x" are the space coordinates, and "t" is time.

We can interpret this as its motion caused by an object's interaction with gravity. Gravity will strongly hold an object in this motion, and it will resist a change to this motion. You can perceive this by the fact that an external non-gravity force will be needed to alter this motion.

Both mass and weight are fully accounted for by this resistance to change the motion as predicted by Einstein's equation.

Note that this perspective is at odds with all modern interpretations of Einstein's Theory of Gravity, or his General Theory of Relativity. For instance, (A) the Higgs Field is currently believed to be the force field that causes an object to have mass. And so (B), the Higgs Boson is said to be responsible for giving objects their mass.

In my interpretation, it is the GRAVITON that causes both mass and weight.