Originally Posted by
Retro Grouch
Also many of those parts, like the stem and seatpost, were Schwinn's own special size.
That's the kicker right there. Even if you are willing to spend the money on newer, lighter components, current parts probably won't fit.
I agree with the posters above. Either ride the bike as is, with the possible exception of fitting new tires and brake pads, or sell it and buy a more suitable newer bike.