Etymology
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withy (n.)

Old English wiðig "willow, willow twig," from Proto-Germanic *with- "willow" (source also of Old Norse viðir, Danish vidje, Swedish vide, Old High German wida, German Weide "willow"), from PIE root *wei-  "to bend, twist" (source also of Avestan vaeiti- "osier," Greek itea "willow," Latin vītis "vine," Lithuanian vytis "willow twig," Polish witwa, Welsh gwden "willow," Russian vitvina "branch, bough").

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willow (n.)
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.
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*wei- 

also weiə-, Proto-Indo-European root meaning "to turn, twist, bend," with derivatives referring to suppleness or binding. 

It forms all or part of: ferrule; garland; iridescence; iridescent; iris; iridium; vise; viticulture; wire; withe; withy.

It is the hypothetical source of/evidence for its existence is provided by: Avestan vaeiti- "osier;" Greek itea "willow," iris "rainbow;" Latin viere "to bend, twist," vitis "vine;" Lithuanian vytis "willow twig;" Old Irish fiar, Welsh gwyr "bent, crooked;" Polish witwa, Welsh gwden "willow," Russian vitvina "branch, bough;" Old English wir "metal drawn out into a fine thread." 

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reluctance (n.)

1640s, "act of struggling against;" 1660s, "unwillingness, aversion;" from the obsolete verb reluct "to strive, struggle, or rebel against" (15c.), from Latin reluctari, reluctare "to struggle against, resist, make opposition," from re- "back, against, in opposition" (see re-) + luctari "to struggle, wrestle," from Proto-Italic *lukto-, from PIE *lug-to- "bent" (source also of Old Irish foloing "supports," inloing "connects;" Middle Welsh ellwng- "to set free;" Greek lygos "withy, pliant twig," lygizein "to bend, twist;" Gothic galukan "to shut," uslukan "to open;" Old English locc "twist of hair."

Related: Reluctancy (1620s.); Bacon (1605) has reluctation.

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