sheet (n.1)

Old English sciete (West Saxon), scete (Mercian) "cloth, covering, towel, shroud," from Proto-Germanic *skautjon-, from *skauta- "project" (source also of Old Norse skaut, Gothic skauts "seam, hem of a garment;" Dutch schoot; German Schoß "bosom, lap"), from PIE root *skeud- "to shoot, chase, throw."

Sense of "piece of paper" first recorded c. 1500; that of "any broad, flat surface" (of metal, open water, etc.) is from 1590s. Of falling rain from 1690s. Meaning "a newspaper" is first recorded 1749. Sheet lightning is attested from 1794; sheet music is from 1857. Between the sheets "in bed" (usually with sexual overtones) is attested from 1590s; to be white as a sheet is from 1751. The first element in sheet-anchor (late 15c.) appears to be a different word, of unknown origin.

sheet (n.2)

"rope that controls a sail," late 13c., shortened from Old English sceatline "sheet-line," from sceata "lower part of sail," originally "piece of cloth," from same root as sheet (n.1). Compare Old Norse skaut, Dutch schoot, German Schote "rope fastened to a sail."

This probably is the notion in phrase three sheets to the wind "drunk and disorganized," first recorded 1812 (in form three sheets in the wind), an image of a sloop-rigged sailboat whose three sheets have slipped through the blocks are lost to the wind, thus "out of control." Apparently there was an early 19c. informal drunkenness scale in use among sailors and involving one, two, and three sheets, three signifying the highest degree of inebriation; there is a two sheets in the wind from 1813.

It must not be wondered at that the poor, untutored, savage Kentuckyan got "more than two thirds drunk," that is, as the sailors term it, three sheets in the wind and the fourth shivering, before the dinner was ended. [Niles' Weekly Register, May 2, 1812]

Definitions of sheet
sheet (n.)
any broad thin expanse or surface;
a sheet of ice
sheet (n.)
paper used for writing or printing;
Synonyms: piece of paper / sheet of paper
sheet (n.)
bed linen consisting of a large rectangular piece of cotton or linen cloth; used in pairs;
Synonyms: bed sheet
sheet (n.)
(mathematics) an unbounded two-dimensional shape;
Synonyms: plane
sheet (n.)
newspaper with half-size pages;
Synonyms: tabloid / rag
sheet (n.)
a flat artifact that is thin relative to its length and width;
Synonyms: flat solid
sheet (n.)
(nautical) a line (rope or chain) that regulates the angle at which a sail is set in relation to the wind;
Synonyms: tack / mainsheet / weather sheet / shroud
sheet (n.)
a large piece of fabric (usually canvas fabric) by means of which wind is used to propel a sailing vessel;
Synonyms: sail / canvas / canvass
sheet (v.)
come down as if in sheets;
The rain was sheeting down during the monsoon
sheet (v.)
cover with a sheet, as if by wrapping;
sheet the body