It can be demonstrated quite readily.
Look at the sun.
Well, get some good welder's goggles, then look at the sun in the sky.
We know how long that light you see takes to get to the earth. (approx 8 mins if I recall correctly).
If you calculate out the motions of the sun, and earth, the gravitational effects you feel from the sun (this effects where the earth is in its orbit amongst other things), the sun is not in the position it ought to be by virtue of the gravity we feel from it.
This is because the effects of gravity travel faster than light.
“If you calculate out the motions of the sun, and earth, the gravitational effects you feel from the sun (this effects where the earth is in its orbit amongst other things), the sun is not in the position it ought to be by virtue of the gravity we feel from it.”
If I’m understanding you correctly, you mean that the apparent visual position of the sun (transmitted by the light) is different from its actual position, deduced from gravitational effects. That alone demonstrates nothing, since it does not mean that any actual “motion” of gravity has occcurred, and without even being able to demonstrate motion, you can’t hope to make any conclusions about the velocity.
In fact, if gravity worked the way you propose, it would have to have an infinite velocity, since its effects are instantaneously apparent at any distance (if you can detect them). Anything with an infinite velocity would also have to be ever present in every location in the universe equally, so we would all experience the exact same gravitational effects as everywhere else. Since that is not the case, then it is apparent that gravity can’t work that way.