awake (awoke, awoken) – будить, просыпаться.

awake (v.) (сочетание двух глаголов из среднеанглийского – в смысле «подниматься» и в смысле «слабый). Да, фантазия у людей работает.
a merger of two Middle English verbs: 1. awaken, from Old English awæcnan (earlier onwæcnan; strong, past tense awoc, past participle awacen) "to awake, arise, originate," from a "on" + wacan "to arise, become awake" (see wake (v.)); and 2. awakien, from Old English awacian (weak, past participle awacode) "to awaken, revive; arise; originate, spring from," from a "on" (see a (2)) + wacian "to be awake, remain awake, watch" (see watch (v.)).

Both originally were intransitive only; the transitive sense being expressed by Middle English awecchen (from Old English aweccan) until later Middle English. In Modern English, the tendency has been to restrict the strong past tense and past participle (awoke, awoken) to the original intransitive sense and the weak inflection (awakened) to the transitive, but this never has been complete (see wake (v.); also cf. awaken).

wake (v.) (будить, просыпаться)
"to become awake," Old English wacan "to become awake," also from wacian "to be or remain awake," both from Proto-Germanic *waken (cf. Old Saxon wakon, Old Norse vaka, Danish vaage, Old Frisian waka, Dutch waken, Old High German wahhen, German wachen "to be awake," Gothic wakan "to watch"), from PIE root *weg- "to be strong, be lively" (cf. Sanskrit vajah "force, swiftness, race, prize," vajayati "drives on;" Latin vegere, vigere "to be live, be active, quicken," vigil "awake, wakeful," vigor "liveliness, activity"). Causative sense "to rouse from sleep" is attested from c.1300. Related: Waked; waking. Phrase wake-up call is attested from 1976, originally a call one received from the hotel desk in the morning.

wake (n.2) (состояние просыпания)
"state of wakefulness," Old English -wacu (as in nihtwacu "night watch"), related to watch; and partly from Old Norse vaka "vigil, eve before a feast," related to vaka "be awake" (cf. Old High German wahta "watch, vigil," Middle Dutch wachten "to watch, guard;" see wake (v.)). Meaning "a sitting up at night with a corpse" is attested from early 15c. (the verb in this sense is recorded from mid-13c.). The custom largely survived as an Irish activity. Wakeman (c.1200), which survives as a surname, was Middle English for "watchman."
watch (v.) (просыпаться, бодрствовать)
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.

watch (n.)
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 meaning "small timepiece" is from 1580s, developing from that of "a clock to wake up sleepers" (mid-15c.).

Это опять русское «вижу», «видишь». Видишь – ВДШ – замена «д» - «t» и «ш» - (sh) – ch – WDSH – WDCH. И PIE корень *weg – быть сильным, оживленным здесь не причем. Такой корень «вг»/ «вж» действительно есть, например русское слово «вага» - вес, откуда «важный», «отважный», «вежа», но здесь он не применим.

1826:
WAKE, to raise from sleep, to rouse. G. and Swed. “waka”; M.G. “wakan”; S. “wacian”; D. “wakke”, B. “waaken”; T. “wachen”.
Не забывайте о переходах букв – к-с-г-ж-з-ш-ч.

WATCH, forbearance from sleep, a night guard to call the hours, a pocket time-piece; G. “vauk”; Swed. “wakt”; S. “wœcce”; T “wacht”; F. “guet”