The rings are even thinner than paper thin. The average thickness of the rings is in the order of 20 meters, with occasional boulders towering 1KM above the ring plane.
Back a million years ago when I was in school there was a debate if they weighed as much as Mimas or much less. The smallest they were saying back then was that the rings had the equivalent mass of a 100km diameter moon. Now, it looks like 50km.