Old English nunne "woman devoted to religious life under vows of celibacy, poverty, and obedience to a superior," also "vestal, pagan priestess," from Late Latin nonna "nun, tutor," originally (along with masc. nonnus) a term of address to elderly persons, perhaps from children's speech, reminiscent of nana (compare Sanskrit nona, Persian nana "mother," Greek nanna "aunt," Serbo-Croatian nena "mother," Italian nonna, Welsh nain "grandmother;" see nanny).
introduced 1947 (at 14th conference of the Union Internationale de Chimie) as a prefix for units of one thousand-millionth part (now "one-billionth"), from Greek nanos "a dwarf." According to Watkins, this is originally "little old man," from nannos "uncle," masc. of nanna "aunt" (see nana), but Beekes calls it "An onomatopoeic word of unknown origin." Earlier nano- was used as a prefix to mean "dwarf, dwarfish," and still it is used in a non-scientific sense of "very small."
"children's nurse," 1795, from the widespread child's word for "female adult other than mother" (compare Greek nanna "aunt," and see nana). The word also is a nickname form of the fem. proper name Ann, which probably is the sense in nanny-goat "female goat" (1706, compare billy-goat). Nanny-house "brothel" is slang from c. 1700. Nanny state, in reference to overintrusive government policies is attested by 1987, the term is associated with British political leader Margaret Thatcher, who criticized the tendency. Nannyism in reference to actions or policies considered unduly protective is by 1959; also compare the verb.