The best fit we have today is that a gravitational wave propagates at the speed of light. Two experiments that validated General Relativity over Newton's theory (Law) were the measurements of the deflection of light by our sun and the precession of the orbit of the planet Mercury.
I am aware that the last two disprove the formula of gravitation given by Newton. However, my thinking is that while such a view of gravitation may fit better with relativity, that such has not been proven yet. It probably does fit better with other things we have learned since, but better fit is again an assumption. My question was more regarding experimental evidence and how such an experiment could be accomplished.