On the fabric of space-time, what is the resisting force? Starting with the typical visualization taught in schools or documentaries: A heavy object is placed in the middle of a canvas, which is bent downwards in the middle, then other objects placed on the canvas move towards the heavy objects etc…
I know that this canvas example doesn’t intent to be accurate, but rather helps to visualize and explain the core mechanism, but still I would like to know something based on it:
What is the equivalent in the universe for the resisting force of the canvas?
Is it more like that space-time has a kind of rigidity/elasticity? (meaning the canvas is stretching)
Or is it more like that space-time can be added or removed from a system? (Meaning the canvas cannot be stretched, but just more is moved inside the system.)
Or something different? - and if what would be a good way visualizing it?
 A: Spacetime has infinite elasticity as such in general relativity, although I think I remember Feynman discussing theoretical alternatives in one of his books. If by resistance you meant why mass only causes finite curvature at $r>0$ (inertia would be a better analogy), the reason is that $G$ is a finite coefficient in the Einstein field equations of general relativity.
A: Following up on @J.G., the gravitational constant G is the critical number that determines how strong gravity is, or equivalently, how much spacetime curves for some amount of mass or energy. One can in fact rigorously get invariant numbers (i.e., not dependent on the coordinate system, and this some measure of its rigidity or flexibility) for the spacetime curvature for any spacetime. For instance, if G were to be zero no amount of mass or energy would cause any spacetime curvature. If G was very large, masses would attract each other much more (thinking in terms of Newtonian gravity), or equivalently a mass (or any amount of energy) would cause much more spacetime curvature. 
If G had been much larger the universe when it started would have self attracted so much that it would have formed a Black Hole before expanding. The universe would have been inside its Black Hole horizon, and collapsed back down. Maybe it would have never even started. The universe as we know it or anything like it would not exist. 
Even if G was not that large, but significantly larger than it is, stars or galaxies would have formed much sooner, be much more massive, and the universe would have expanded some and then collapsed again in a Big Crunch. If G had been weaker than it is, galaxies and stars may not have formed, and w would not be around. 
If you compared G with the equivalent in electromagnetism or nuclear forces, their so called coupling constants, or some of the strengths of their forces for comparable particles, gravity of many orders of magnitude weaker than electromagnetism. However, it is purely (except for dark energy) and mostly attractive, so it can form galaxies and stars. The other forces in some cases attract and in others repeal. You can see the comparative magnitudes of the different forces at Wikipedia at https://en.m.wikipedia.org/wiki/Fundamental_interaction
So, the values of the coupling constants, and a few other parameters like the mass of the electron, proton and neutron, go a long way towards making our universe possible, and for us livable. In reality you need to consider other constants besides those, but it's known that a lot of different numbers would have made our universe impossible. G is hugely important in the overall evolution of the universe. 
