Your question as to HOW gravity affects space-time is similar to the following questions...to use some of your examples.
What is mass?
Why doesn't greater mass and greater acceleration cause LESS force as opposed to MORE force (i.e why isn't the equation F=1/ma instead F=ma
Why does light travel at a constant speed (instead of infinitely)?
All of these questions don't really have answers per se.
We only know of their existence and how they work by observation. We don't know why they work, they just do. For example, you can demonstrate that F=ma by experimentation, but you can't explain WHY that equation exists in the first place. It just does.
Remember, this is HT, so plz no flamewars based on the next comments...
There are pretty much two theories on the overall HOW of something.
1. Within the overall nothingness of nothing, the eventuality of certain immutable laws of Physics are just there. Things like, Mass affects Space-Time, The speed of light is constant in a vaccum, etc. They are simply immutable facets of the reality of the Universe that sprang into existence for some reason with these laws in place. The Universe IS defined by these immutable laws that exist within it.
OR
2. A Divine being created the Universe establishing all of the relationships and effects of these immutable laws that he designed so that reality as we understand it could take place. Again, these laws are immutable, they simply are, because he chose them to be that way.
In either of these scenarios, there will still be postulates, ideas that cannot be proven scientifically, they can merely be demonstrated to be accurate all of the time. A good example of this is Pythagorean (Planar) vs. Euclidean (Spherical) geometry. There are postulates within each field that form the basis of each that cannot be true within the other. You cannot prove these postulates, they simply are in order for the rest of the proveable things to take place.
P-X