Fiorino Grosso da 2 Soldi detto Popolino databile al I semestre 1369 Zecca: Firenze - Fronte: giglio fiorentino - Retro: San Giovanni Battista stante di fronte alza la mano destra nell'atto di benedire e tiene una lunga croce con la mano sinistra - gr. 1,00 - Rara - Simbolo corona (Niccolò di Bocchino di Rimbaldese) - Da e
I know this is a very old thread, but I know the OP is still active here.
I've been learning about medieval Florence silver recently, and another option for your coin is a quattrino of Florence.
The quattrino had a 3/4 figure of St. John, and is small, under 1 g., and about 18 mm. The grosso usually has a full-length figure of St. John (except in early 1400s where he is seated) , typically 22-24 mm and 2 - 2.5 g.