Origin and history of outwatch

Middle English wacchen, from Old English wæccan "keep watch, be awake," from Proto-Germanic *wakjan, from PIE root *weg- "to be strong, be lively." Essentially the same word as Old English wacian "be or remain awake" (see wake (v.)); perhaps a Northumbrian form of it.

The meaning "be vigilant" is from c. 1200. That of "to guard (someone or some place), stand guard" is late 14c. The sense of "to observe, keep under observance" is mid-15c. To watch out "be on one's guard" is by 1845, U.S. colloquial. Watch it! as a warning is attested by 1916. Related: Watched; watching.

in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."

In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]