TW-
These Sun Comfort Rover Sport 21 speeds I use (pix 1/2/3) are really light, but I just looked in the catalog and they don't show a shipping weight. They are easy to pick up with one hand, by far the lightest frame I've found.
(Sun's Website might have the details, but it runs too slow for my computer to access).
My steel rear wheels/tire/tubes weigh in at 9 pounds, you could shave some weight off by using aluminum instead of steel and not use the heavy punctureproofs, get it down to 5 pounds or so.
And don't use the 12" saddles, because they must weigh 2-3 pounds.
They are identical to a Diamondback model, for $100 cheaper, my bike shop sells them to me for $340 (with the heavier wheel). Bike shops don't display generic Suns, but they are in the J & B catalog.
Note how the pedals are pushed forward 6 inches, the seat post is tilted back a bit, and the handlebars have 3 adjustment settings, so you can really get into a "lowrider" kind of feel.
Pic 4 is a Columbia 21 speed, the guy got it for $100 online (NEW), as I understand it, they normally are over $300 also. But it was also lightweight.