So I see two alternatives:
1. Search the literature for experiments, perhaps ongoing, that determine if gravity is instantaneous or not. That can be your task, as well as mine
2. Do some gadanken(sp?) (thought) experiments. For example:
(i) Suppose that gravity and all other forces traveled only at the speed of light and see if any contradictions can be found:
(a) black holes would not be detectable
(b) gravity would be red shifted
(c) particles could not be entangled
The ball is yours.
PS: The experiments done by Alan Aspect in France first proved, based on the math of Bell, that quantum mechanics is correct and the prediction of Relativity that all forces travel at the speed of light or less is incorrect. This experiment has been repeated many times and the results are always the same.
Alan created an photon pair of opposite spin at a point and allowed them to propagate off in opposite dirtections. He then measured the spin on one, thereby collapsing the waves into a photon of definite spin. Depending on the arrangement of the apparatus, the spin measured was not always the same in agreement with quantum mechanics. But the spin of the other photon was always opposite, proving that one particle had instantanewous knowledge of the other.
This experiment has been repeated with electron-positron pairs, and even molecule pairs with some property that is opposite. The result is always the same. The speed of light is broken and within the limits of the measurements, the action appears to be instantaneous.
Now my explanation for how this happens is that the two particles are connected in higher dimensions. In string theory fermions are made in ten dimensions- but 6 of them compactify down to 4-d spacetime. These compactifies dimensions then form a thread that connects say the e-p pair to each other so that one always knows the state of the other.
Now this same argument can be extended to spacetime itself. The particles of space have zero mass. Therefore their wave functions are infinite just like a photon. Did you know that photons do not experience the passage of time. They retain the time of their creation as a marker. So if you ask how big is the photon at any particular time, it eithre does not exist or it is infinite, like a delta function.
Any zero mass particle has the same property from quantum mechanics- their wave functions are infinite. Therefore all the wave functions of space particles overlap and each partilce knows what happens to every other pertice instantly, just like in the Alan Aspect experiment. It's called 'entanglement'.
That is how space reacts instantly. And since gravity is just spacetime curvature according to General Relativity, gravity propagates instantly. We call it propagation by virtaul particles. But nthat is misleading. In my opinion, it all happens because of entanglement, which has been proven experimentally.