'baya' originates from Hindi/Urdu, specifically the word 'baiyā' (or variants), used locally for the weaverbird and adopted into English in the 18th–19th century by naturalists.

'baya' entered English from Hindi/Urdu 'baiyā' (a local name for the bird) through colonial-era natural history reports and eventually became the modern English name 'baya'.

Initially, it was a local name for the specific weaverbird; over time it was adopted into English with the same meaning, referring generally to that species of weaverbird.