"flexible and graceful," 1791, from willow + -y (2). Earlier "bordered or shaded by willows" (1751). Willowish is older (1650s) but only in reference to the color of willow leaves. Related: Willowiness.
Old English welig "willow," from Proto-Germanic *wel- (source also of Old Saxon wilgia, Middle Dutch wilghe, Dutch wilg), probably from PIE root *wel- (3) "to turn, revolve," with derivatives referring to curved, enclosing objects. The change in form to -ow (14c.) paralleled that of bellow and fellow. The more typical Germanic word for the tree is represented by withy.
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
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Harper, D. (n.d.). Etymology of willowy. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/willowy