Everyone knows I am a sucker for old Bianchis, but ...
I have never seen an Italian-made Biachi with stem shifters. I'll bet your bottom bracket is English-threaded, which implies Taiwan manufacture. If so, do not invest too much money in it. If you can find a good 5- or 6-speed wheelset on eBay or at a yard sale, that is probably the best upgrade you can make. Friction downtube levers or old ratcheted SunTour barcons would be an improvement over those that stem-mounted castration system.
Although a lightweight bicycle is indeed a pleasure to ride, a few pounds of surplus nonrotating weight is not that big a deal for the nonracer.
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"Far and away the best prize that life offers is the chance to work hard at work worth doing." --Theodore Roosevelt
Capo: 1959 Modell Campagnolo, S/N 40324; 1960 Sieger (2), S/N 42624, 42597
Carlton: 1962 Franco Suisse, S/N K7911
Peugeot: 1970 UO-8, S/N 0010468
Bianchi: 1982 Campione d'Italia, S/N 1.M9914
Schwinn: 1988 Project KOM-10, S/N F804069