It derives from the predominantly Lombard and Milanese use of attributing to sons without a father a well-to-do surname such as Diotallevi, Diotaiuti that by contraction then became simply Allevi, etc. In the Marche and more precisely in Offida (AP) we have already found from the 1200s a Allevi family rich and of noble lineage, which already back then had ancient origins. A Giacomo dict Allevi (so indicated in the documents), a native of Offida, was prior of the Augustinian convent of Lanciano (CH).
You may be interested
Verba Volant, Scripta Manent