The Law of "Universal Gravitation" was "discovered" by Isaac Newton using data about the motion of the planets according to the heliocentric model of the Solar System and applying his famous laws of motion to these motions. Then, people thought they should prove this idea between terrestrial objects. As you may or may not know the heliocentric model of the solar system assumes, among other things, that the Earth is round. So, one cannot use the Law of Universal Gravitation as a proof of round earth simply because one of the assumptions incorporated into it is the assumption of a Round Earth.