Speaking in general, sound waves will propagate through a light, stiff material with less resistance than they will through a heavy, limp one; there is a huge body of research on this subject, and its relation to perceived sound quality. Mahogany, in particular, has higher value as a tone wood if it is lighter and less dense, but much of the quality, light, old-growth timber has been harvested.
A point of reference here is that Stradivarii and Del Gesus (Guarnerii), which are considered among the best-toned of violins, were constructed with light, stiff wood grown during the Maunder Minimum (or "little ice age", in the mid-1600s to the early 1700s). Similarly, swamp ash is considered a good tone wood; it seems that its tonal characteristics depend in large part upon its having grown in conditions which allow it to become very light and yet retain stiffness - the parts which grew under water, IIRC.
That said, I have heard a stone guitar which sounded very good, and it was certainly not light, though it was stiff!
Also, tone is a highly subjective thing; people can have very different -but equally valid- ideas on what constitutes "good tone".