Etymology 1 
From Middle English shere, scheere, schere, skere, from Old English *scǣre; merged with Middle English shire, schire, schyre, shir, from Old English scīr (“clear, bright; brilliant, gleaming, shining, splendid, resplendent; pure”) and Old Norse skírr (“pure, bright, clear”), both from Proto-Germanic *skīriz (“pure, sheer”) and *skairiz, from Proto-Indo-European *sḱēy- (“luster, gloss, shadow”). Cognate with Danish skær, German schier (“sheer”), Dutch schier (“almost”), Gothic 𐍃𐌺𐌴𐌹𐍂𐍃 (skeirs, “clear, lucid”). Outside Germanic, cognate to Albanian hirrë (“whey, serum”).
- (textiles) Very thin or transparent.
- Her light, sheer dress caught everyone’s attention.
- 1954, Alexander Alderson, chapter 17, The Subtle Minotaur:
- “She sheathed her legs in the sheerest of the nylons that her father had brought back from the Continent, and slipped her feet into the toeless, high-heeled shoes of black suède.”
- Pure; unmixed; being only what it seems to be.
- I think it is sheer genius to invent such a thing.
- This poem is sheer nonsense.
- 2012, July 15. Richard Williams in Guardian Unlimited, Tour de France 2012: Carpet tacks cannot force Bradley Wiggins off track
- Cycling's complex etiquette contains an unwritten rule that riders in contention for a race win should not be penalised for sheer misfortune.
- Very steep; almost vertical or perpendicular.
- It was a sheer drop of 180 feet.
- Used to emphasize the amount or degree of something.
- Through technological wizardry and sheer audacity, Google has shown how we can transform the intellectual riches of our libraries...
- 2012 October 31, David M. Halbfinger, "," New York Times (retrieved 31 October 2012):
- Perhaps as startling as the sheer toll was the devastation to some of the state’s well-known locales. Boardwalks along the beach in Seaside Heights, Belmar and other towns on the Jersey Shore were blown away. Amusement parks, arcades and restaurants all but vanished. Bridges to barrier islands buckled, preventing residents from even inspecting the damage to their property.
- (very thin or transparent): diaphanous, see-through, thin
- (pure, unmixed): downright, mere, pure, undiluted, unmitigated
- (straight up and down): perpendicular, steep, vertical
Etymology 2 
sheer (plural sheers)
- (nautical) The curve of the main deck or gunwale from bow to stern.
- (nautical) An abrupt swerve from the course of a ship.
- (chiefly nautical) To swerve from a course.
- A horse sheers at a bicycle.
- (obsolete) To shear.
- (Can we find and add a quotation of Dryden to this entry?)
Part or all of this entry has been imported from the 1913 edition of Webster’s Dictionary, which is now free of copyright and hence in the public domain. The imported definitions may be significantly out of date, and any more recent senses may be completely missing.