Etymology
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sheer (adj.)
c. 1200, "exempt, free from guilt" (as in Sheer Thursday, the Thursday of Holy Week); later schiere "thin, sparse" (c. 1400), from Old English scir "bright, clear, gleaming; translucent; pure, unmixed," and influenced by Old Norse cognate scær "bright, clean, pure," both from Proto-Germanic *skeran (source also of Old Saxon skiri, Old Frisian skire, German schier, Gothic skeirs "clean, pure"), from PIE root *sker- (1) "to cut."

Sense of "absolute, utter" (sheer nonsense) developed 1580s, probably from the notion of "unmixed;" that of "very steep" (a sheer cliff) is first recorded 1800, probably from notion of "continued without halting." Meaning "diaphanous" is from 1560s. As an adverb from c. 1600.
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sheer (v.)
1620s, "deviate from course" (of a ship), of obscure origin, perhaps from Dutch scheren "to move aside, withdraw, depart," originally "to separate" (see shear (v.)). Related: Sheered; shearing. As a noun from 1660s.
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*sker- (1)

also *ker-, Proto-Indo-European root meaning "to cut."

It forms all or part of: bias; carnage; carnal; carnation; carnival; carnivorous; carrion; cenacle; charcuterie; charnel; corium; cortex; crone; cuirass; currier; curt; decorticate; excoriate; incarnadine; incarnate; incarnation; kirtle; scabbard; scar (n.2) "bare and broken rocky face of a cliff or mountain;" scaramouche; scarf (n.2) "connecting joint;" scarp; score; scrabble; scrap (n.1) "small piece;" scrape; screen; screw; scrimmage; scrofula; scrub (n.1) "low, stunted tree;" scurf; shard; share (n.1) "portion;" share (n.2) "iron blade of a plow;" sharp; shear; shears; sheer (adj.) "absolute, utter;" shirt; shore (n.) "land bordering a large body of water;" short; shrub; skerry; skirmish; skirt.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit krnati "hurts, wounds, kills," krntati "cuts;" Hittite karsh- "to cut off;" Greek keirein "to cut, shear;" Latin curtus "short;" Lithuanian skiriu, skirti "to separate;" Old English sceran, scieran "to cleave, hew, cut with a sharp instrument;" Old Irish scaraim "I separate;" Welsh ysgar "to separate," ysgyr "fragment."

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pantyhose (n.)

 "sheer tights or close-fitting legwear covering the body from the waist to the toes," 1963, also pantihose; see panties + hose (n.).

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bare (adj.)
Old English bær "naked, uncovered, unclothed," from Proto-Germanic *bazaz (source also of German bar, Old Norse berr, Dutch baar), from PIE *bhoso- "naked" (source also of Armenian bok "naked;" Old Church Slavonic bosu, Lithuanian basas "barefoot"). Meaning "sheer, absolute" (c. 1200) is from the notion of "complete in itself."
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chiffon (n.)

1765, "feminine finery, something used by women purely for adornment," from French chiffon (17c.), diminutive of chiffe "a rag, piece of cloth" (17c.), which is of unknown origin, perhaps a variant of English chip (n.1) or one of its Germanic cousins. Klein suggests Arabic. Meaning "sheer silk fabric, thin gauze" is from 1890. Extension to pastry is attested by 1929, probably on the notion of "lightness."

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very (adj.)
late 13c., verray "true, real, genuine," later "actual, sheer" (late 14c.), from Anglo-French verrai, Old French verai "true, truthful, sincere; right, just, legal," from Vulgar Latin *veracus, from Latin verax (genitive veracis) "truthful," from verus "true" (source also of Italian vero), from PIE root *were-o- "true, trustworthy." Meaning "greatly, extremely" is first recorded mid-15c. Used as a pure intensive since Middle English.
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stark (adj.)

Old English stearc "stiff, strong, rigid, obstinate; stern, severe, hard; harsh, rough, violent," from Proto-Germanic *starka- (source also of Old Norse sterkr, Danish, Old Frisian sterk, Middle Dutch starc, Old High German starah, German stark, Gothic *starks), from PIE root *ster- (1) "stiff." From the same root as stern (adj.).

Meaning "utter, sheer, complete" first recorded c. 1400, perhaps from influence of common phrase stark dead (late 14c.), with stark mistaken as an intensive adjective. Sense of "bare, barren" is from 1833. As an adverb from c. 1200. Related: Starkly; starkness. Stark-raving (adj.) is from 1640s; earlier stark-staring 1530s.

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pure (adj.)

mid-13c., of gold, "unalloyed;" c. 1300 "unmixed, unadulterated; homogeneous," also "total, complete, absolute; bare, mere," also "sexually pure, virgin, chaste" (late 12c. as a surname, and Old English had purlamb "lamb without a blemish"), from Old French pur "pure, simple, absolute, unalloyed," figuratively "simple, sheer, mere" (12c.), from Latin purus "clean, clear; unmixed; unadorned; chaste, undefiled."

This is conjectured to be from PIE root *peue- "to purify, cleanse" (source also of Latin putus "clear, pure;" Sanskrit pavate "purifies, cleanses," putah "pure;" Middle Irish ur "fresh, new;" Old High German fowen "to sift").

It replaced Old English hlutor. The meaning "free from moral corruption" is recorded from mid-14c. In reference to bloodlines, attested from late 15c. In music, "mathematically perfect," by 1872.

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mere (adj.)

late 14c., of a voice, "pure, clear;" mid-15c., of abstract things, "absolute, sheer;" from Old French mier "pure" (of gold), "entire, total, complete," and directly from Latin merus "unmixed" (of wine), "pure; bare, naked;" figuratively "true, real, genuine," according to some sources probably originally "clear, bright," from PIE *mer- "to gleam, glimmer, sparkle" (source also of Old English amerian "to purify," Old Irish emer "not clear," Sanskrit maricih "ray, beam," Greek marmarein "to gleam, glimmer"). But de Vaan writes "there is no compelling reason to derive 'pure' from 'shining,'" and compares Hittite marri "just so, gratuitously," and suggests the source is a PIE *merH-o- "remaining, pure." 

The English sense of "nothing less than, in the fullest sense absolute" (mid-15c., surviving now only in vestiges such as mere folly) existed for centuries alongside the apparently opposite sense of "nothing more than" (1580s, as in a mere dream).

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