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Old English wæccan "keep watch, be awake," from Proto-Germanic *wakojan; essentially the same word as Old English wacian "be or remain awake" (see wake (v.)); perhaps a Northumbrian form. Meaning "be vigilant" is from c.1200. That of "to guard (someone or some place), stand guard" is late 14c. Sense of "to observe, keep under observance" is mid-15c. Related: Watched; watching.
Old English wæcce "a watching," from wæccan (see watch (v.)). Sense of "sentinel" is recorded from c.1300; that of "person or group officially patroling a town (especially at night) to keep order, etc." is first recorded 1530s. Meaning "period of time in which a division of a ship's crew remains on deck" is from 1580s. Sense of "period into which a night was divided in ancient times" translates Latin vigilia, Greek phylake, Hebrew ashmoreth.
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]The meaning "small timepiece" is from 1580s, developing from that of "a clock to wake up sleepers" (mid-15c.).