1660s, according to OED, most likely a diminutive and contraction of grannam, shortened form of grandame, rather than from grandmother. The sailor's granny knot (by 1803), originally granny's knot, readily jammed and insecure, so called because "it is the natural knot tied by women or landsmen" [Smyth, "Sailor's Word-Book," 1867]. Granny Smith apples (1895) named for Maria Ann Smith (d.1870) of Australia, who originated them.