Old English wæcce "a watching, state of being or remaining awake, wakefulness;" also "act or practice of refraining from sleep for devotional or penitential purposes;" from wæccan "keep watch, be awake," from Proto-Germanic *wakjan, from PIE root *weg- "to be strong, be lively."
From c. 1200 as "one of the periods into which the night is divided," in reference to ancient times translating Latin vigilia, Greek phylake, Hebrew ashmoreth. From mid-13c. as "a shift of guard duty; an assignment as municipal watchman;" late 13c. as "person or group obligated to patrol a town (especially at night) to keep order, etc."
Also in Middle English, "the practice of remaining awake at night for purposes of debauchery and dissipation;" hence wacches of wodnesse "late-night revels and debauchery." The alliterative combination watch and ward preserves the old distinction of watch for night-time municipal patrols and ward for guarding by day; in combination, they meant "continuous vigilance."
Military sense of "military guard, sentinel" is from late 14c. General sense of "careful observation, watchfulness, vigilance" is from late 14c.; to keep watch is from late 14c. Meaning "period of time in which a division of a ship's crew remains on deck" is from 1580s. The meaning "small timepiece" is from 1580s, developing from that of "a clock to wake up sleepers" (mid-15c.).
The Hebrews divided the night into three watches, the Greeks usually into four (sometimes five), the Romans (followed by the Jews in New Testament times) into four. [OED]
On þis niht beð fowuer niht wecches: Biforen euen þe bilimpeð to children; Mid-niht ðe bilimpeð to frumberdlinges; hanecrau þe bilimpeð þowuene men; morgewile to alde men. [Trinity Homilies, c. 1200]
"a vigil beside a dying person," 1865, from death + watch (n.) "a watching." The death-watch beetle (1660s) inhabits houses, makes a ticking noise like a pocket-watch, and was superstitiously supposed to portend death.
FEW ears have escaped the noise of the death-watch, that is, the little clicking sound heard often in many rooms, somewhat resembling that of a watch; and this is conceived to be of an evil omen or prediction of some person's death: wherein notwithstanding there is nothing of rational presage or just cause of terror unto melancholy and meticulous heads. For this noise is made by a little sheathwinged grey insect, found often in wainscot benches and wood-work in the summer. [Browne, "Vulgar Errors"]