Etymology
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waver (v.)
late 13c., weyveren, "to show indecision," probably related to Old English wæfre "restless, wavering," from Proto-Germanic *wæbraz (source also of Middle High German wabern "to waver," Old Norse vafra "to hover about"), a frequentative form from the root of wave (v.). Related: Wavered; wavering.
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unwavering (adj.)
1560s, from un- (1) "not" + present participle of waver (v.).
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wobble (v.)
1650s, wabble, probably from Low German wabbeln "to wobble;" cognate with Old Norse vafla "hover about, totter," related to vafra "move unsteadily," from Proto-Germanic *wab- "to move back and forth," perhaps from PIE *webh- "to weave" (see waver). Form with -o- is from 1851. Related: Wobbled; wobbling. The noun is attested from 1690s.
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vacillation (n.)

c. 1400, "hesitation, uncertainty," from Latin vacillationem (nominative vacillatio) "a reeling, wavering," noun of action from past-participle stem of vacillare "sway to and fro, waver, hesitate, be untrustworthy," of uncertain origin. Originally in reference to opinion or conduct; literal sense is recorded from 1630s.

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dubitation (n.)

early 15c., dubitacioun, "act or state of doubting," from Old French dubitation (13c.) and directly from Latin dubitationem (nominative dubitatio) "uncertainty, doubt," noun of state from past-participle stem of dubitare "to waver in opinion, be uncertain, doubt, question" (related to dubius "uncertain;" see dubious).

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vacillate (v.)
1590s, "to sway unsteadily," from Latin vacillatus, past participle of vacillare "sway to and fro; hesitate" (see vacillation). Meaning "to waver between two opinions or courses" is recorded from 1620s. Related: Vacillated; vacillates; vacillating.
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vague (adj.)

"uncertain as to specifics," 1540s, from French vague "empty, vacant; wild, uncultivated; wandering" (13c.), from Latin vagus "strolling, wandering, rambling," figuratively "vacillating, uncertain," perhaps from PIE *Huog-o-  and cognate with Old Norse vakka "to stray, hover," Old High German wankon "to totter, stagger," Old High German winkan "to waver, stagger, wink," Old English wincian "to nod" [de Vaan]. Related: Vagueness.

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doubt (v.)

c. 1200, douten, duten, "to dread, fear, be afraid" (a sense now obsolete), from Old French doter "doubt, be doubtful; be afraid," from Latin dubitare "to doubt, question, hesitate, waver in opinion" (related to dubius "uncertain"), from duo "two" (from PIE root *dwo- "two"), with a sense of "of two minds, undecided between two things." Compare dubious. Etymologically, "to have to choose between two things."

The sense of "fear" developed in Old French and was passed on to English. Meaning "to be uncertain, hesitate or waver in opinion" is attested in English from c. 1300. The transitive senses of "be uncertain as to the truth or fact of" and "distrust, be uncertain with regard to" are from c. 1300.

The -b- was restored 14c.-16c. in French and English by scribes in imitation of Latin. French dropped it again in 17c., but English has retained it.

It replaced Old English tweogan (noun twynung), from tweon "two," on notion of "of two minds" or the choice between two implied in Latin dubitare. Compare German Zweifel "doubt," from zwei "two."

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flaunt (v.)
1560s, "to display oneself in flashy clothes," of unknown origin. Perhaps a variant of flout or vaunt. Perhaps from Scandinavian, where the nearest form seems to be Swedish dialectal flankt "loosely, flutteringly," from flakka "to waver" (related to flag (v.1)). It looks French, but it corresponds to no known French word. Transitive sense, "flourish (something), show off, make an ostentatious or brazen display of" is from 1827. Related: Flaunted; flaunting; Flauntingly.
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lapwing (n.)
Middle English lappewinke (late 14c.), lapwyngis (early 15c.), folk etymology alteration of Old English hleapewince "lapwing," probably literally "leaper-winker," from hleapan "to leap" (see leap (v.)) + wince "totter, waver, move rapidly," related to wincian "to wink" (see wink (v.)).

Said to be so called from "the manner of its flight" [OED] "in reference to its irregular flapping manner of flight" [Barnhart], but the lapwing also flaps on the ground pretending to have a broken wing to lure egg-hunters away from its nest, which seems a more logical explanation. Its Greek name was polyplagktos "luring on deceitfully."
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