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1884, perhaps from daft (adj.), or from obsolete daffe "halfwit" (cf. 15c. daffish), of unknown origin. With -y (2). Related: Daffily; daffiness.
Crazy; nuts: He tries to convince her that she is not daffy
[1884+; fr British dialect daff, ''fool, simpleton''; daffish is attested fr the 15th century]