The thinnest, most lightweight lenses are typically the most expensive. With high index lenses, it seems that the less you get, the more you pay. Regardless of the index of refraction, plastic high index lenses tend to be lighter in weight than glass high index lenses, simply because plastic weighs less than glass to begin with. Just like high index lenses, aspheric lenses are also thinner than regular lenses. But the thinness is accomplished with the lens design, not just the lens material.
Aspheric lenses use flatter base curves in their design.
In plus lenses for farsighted people, the curves flatten away from the center, for a lens that doesn't bulge out as much. It also doesn't magnify the eye nearly as much as a regular lens design would, so the eye looks more natural. In minus lenses for nearsighted people, the curves steepen away from the center, toward the edge of the lens. This results in a thinner lens edge, even for a strong prescription. Newer aspherics contain the base curves on the back side of the lens, closer to the eye, rather than on the front side.