Most prescription lenses today are made of plastic, and yes it is lighter than glass. The factor that most affects how thin a lens can get (and as lightweight as a result) is using a lens material that as is high index as possible. The second most factor is having the lens made into an aspheric shape. However, having both of these can drive up the cost quite a bit.
Polycarbonate is a high index lens material, though not the highest. Certain optical shops might have a trade name for it, but it would still generically be known as polycarbonate. Polycarbonate is the most commonly used of all high index materials, making it cheaper, widely available, and available in just about any lens design (i.e. bifocals, trifocals, progressives, etc).
Polycarbonate is extremely impact resistant, which also allows it to be thin. In the United States, lenses have to meet a standard for impact resistance, so lenses will be as thick as necessary to meet that standard. For polycarbonate, that's usually a 1.0 mm center thickness for minus lenses, though other high index lens materials can get down to 1.0 mm center thickness too. In other countries it may be possible to get even thinner lenses, as they may not require a standard for impact resistance.
Getting a lens to be made into an aspheric shape requires specific specialized machinery for the lens cutting process, which is why it drives up the cost, however it does allow for thinner lenses as well.
Hope that helps.
