Probably a modification of baby. Popularized in online usage by the "How is babby formed?" meme from the mid-2000s.
babby (plural babbies)
- (UK and US dialects, also Internet slang) A baby (human infant).
- ^ “How is babby formed?”, in Know Your Meme, 2009-05-06
- Joseph Wright, editor (1898), “BABBY, sb.”, in The English Dialect Dictionary: […], volume I (A–C), London: Henry Frowde, […], publisher to the English Dialect Society, […]; New York, N.Y.: G. P. Putnam’s Sons, OCLC 81937840, page 107, column 2.