According to E. Rossoni, it derives from a nickname based on the archaic French term barreque, the current barrique (small barrel or cask), which was formerly a measure of capacity in France equivalent to about 225 litres, possibly attributed as a nickname for a robust build of the founder of the lineage.

According to V. Blunda, it is a Sicilian surname of dialectal origin, formed from a nickname describing the body. It derives from the dialectal word barrèca, meaning "pot-bellied person". As a surname it may have originated in a nickname applied to a person with a prominent abdomen, a common motivation in Sicilian cognomens describing the physique, where visible traits served as a distinctive mark in small communities. It coexists in the island's onomastics with other cognomens referring to the same characteristic, such as Buttiglione, Buzzone or Pantorno.