I haven't seen an F1 tire up close in the last 7 or 8 years, but the last ones I handled were incredibly light. I'm sure the (used) rear I saw was easily less than 20 lbs. In fact, the thing that was most impressive about the tire, was how thin the sidewall was. It seemed as though you could put your finger right through it.
The tread rubber (at least what was left of it) was also so soft that you could scrape chunks of it out of the tread surface with your fingernails. The sidewalls and tread carcass of F1 tires are so thin and light, it's easy to see why they get punctures from running over any debris on the race track.
While F1 tires may seem like the single most high performance application there is, I personally think NASCAR tires are worked harder. Not only are NASCAR tires smaller, they must also have inner liners and they are subjected to much heavier cornering loads. Due to Cup cars being twice as heavy as an F1 car and running at consistently higher cornering speeds.
Of course, f1 tire dimensions (rim diameters and tread widths) are limited by rules.