(From) latin, pensum.
Piece, from https://www.etymonline.com/word/piece#etymonline_v_14956
c. 1200, pece, "fixed amount, measure, portion;" c. 1300, "fragment of an object, bit of a whole, slice of meat; separate fragment, section, or part," from Old French piece "piece, bit portion; item; coin" (12c.), from Vulgar Latin pettia, probably from Gaulish pettsi (compare Welsh peth "thing," Breton pez "piece, a little"), perhaps from an Old Celtic base kwezd-i-, from PIE root kwezd- "a part, piece" (source also of Russian chast' "part").
So yes, it looks like coincidence.
(Peso is a word in Spanish and up until modern times, there's very little transfer from English to Spanish)