fem. pet name, from Bet, shortened from Elizabeth, + -y (3). Also in old slang (by 1857), "man who interferes with the domestic duties of women" [Century Dictionary, 1889].
Entries linking to betty
Elizabeth
fem. proper name, Biblical name of the wife of Aaron, from Late Latin Elisabeth, from Greek Eleisabeth, Eleisabet, from Hebrew Elishebha "God is an oath," the second element said by Klein to be related to shivah (fem. sheva) "seven," and to nishba "he swore," originally "he bound himself by (the sacred number) seven." Has never ranked lower than 26th in popularity among the names given to baby girls in the U.S. in any year since 1880, the oldest for which a reliable list is available. The city in New Jersey is named for Lady Elizabeth Carteret (d.1697), wife of one of the first proprietors of the colony.
-y 3
suffix in pet proper names (such as Johnny, Kitty), first recorded in Scottish c. 1400; according to OED it became frequent in English 15c.-16c. Extension to surnames seems to date from c. 1940. Use with common nouns seems to have begun in Scottish with laddie (1546) and become popular in English due to Burns' poems, but the same formation appears to be represented much earlier in baby and puppy.