If you want a lightweight Schwinn, just look for one not made in Chicago.
Anything "Made in Japan" from the 70s to early 80s, most of the 80s bikes made in Mississippi are competitively lightweight for the era.
There is one Chicago-made, non Paramount that works well (I built one in '00) and that's a fillet brazed Sports Tourer. Not the easiest thing to find, but they're out there.