Did Galileo offer an explanation why his law of falling bodies is independent of mass? Naively, (and endorsed by Aristotle) one expects heavier things to fall more quickly, Galileo Galilei showed in the early modern period, that in fact this is not correct, and that in fact how they fell as independent of mass (if air resistance remained negligible).
Did he offer an explanation of this observation?
 A: Yes--- he argued as follows in Dialogue concerning the Two Principal World Systems: suppose you tie a heavy object to a light one with a rope, would the light object fall slower and retard the heavy object, or would the heavy and light object together be a heavy object that falls more quickly? He concludes that neither: they both fall at the same rate.
This type of philosophical argument is persuasive, but Galileo always backs it up with naive experiments, and naive measurements. Aristotle's views are almost never "naive" in this way, and because of this they are almost never correct! Aristotle was writing for elites, and his pontifications are designed to be erudite and convincing, they are not designed to be correct, or else he would have done the experiment too. His books are ancient coffee-table books, they have no academic value.
Anyone who did the experiment would have seen Galileo is right, it is the non-naive arguments about the medium being the cause of the motion, and the impelling motive forces and desires of objects, that make Aristotle's blatherings both the opposite of naive, and the opposite of correct.
