Very very rare, with a lineage in Udine and others around Italy, it could be of Latin origin and derive from the Roman praenomen Cutius, originated from the Etruscan gens Cutu, of which we have an example in the Annales of Tacitus: ".. .cum velut munere deum tres biremes adpulere ad usus commeantium illo mari. et erat isdem regionibus Cutius Lupus quaestor, which we try to vether ex more calles evenerant ... ", but it is also possible a derivation from the apheresis of a modification of the name Marco , Marcuzzo, dei Marcuzzi, Cuzzi. We find traces of this surname in Rovinj in Istria since the 1600s.
You may be interested
Verba Volant, Scripta Manent