um, 21mm is about as skinny a tire as anyone runs on the street, and thats for like Criterium racing. a 23mm with a 180 lb rider should have 110-120 PSI, I can't imagine what a 20 or smaller would need.
my ~ $500 aluminum framed 'large' size hybrid, with 700x35 tires is 28 lbs the way it came from the factory. thats before I added a speedo, water bottle cage, kryptonite, headlights, etc etc, its about 30 lbs now.
every pound below that, you're talking increasingly serious $$$s. to get to or below 20 lbs, thats almost certainly a full carbon fiber bike, with very light racing wheels. I wanna lose 20 lbs from ME before I start worrying about bicycle weight