once-over (n.)

"one time only; at one time in the past, formerly," c. 1200, anes, basically an adverbial form of one with adverbial genitive -s. The Old English form was æne, but it was replaced by, or reshaped by analogy with, the genitive singular of the early Middle English form of one and the common addition of -es to adverbs at that time. The spelling changed as pronunciation shifted from two syllables to one after c. 1300; the -ce is to retain the breathy -s- (compare hence). The pronunciation change to "wuns" parallels that of one.

As an emphatic, meaning "once and for all," it is attested from c. 1300, but in modern U.S. this is a Pennsylvania German dialect formation. Meaning "in a past time" (but not necessarily just one time) is from mid-13c.

Never once "never at all" is from early 13c. Once in a while "sometimes" is by 1781. Once upon a time as the beginning of a story is recorded from 1590s, earlier once on a time (late 14c.). At once originally (early 13c.) meant "simultaneously," later "in one company" (c. 1300), and preserved the sense of "one" in the word; the phrase typically appeared as one word, atones; the modern meaning "immediately" is attested from 1530s. Once and for all "once as a final act" is from 1848, earlier once for all (late 15c.).

Old English ofer "beyond; above, in place or position higher than; upon; in; across, past; more than; on high," from Proto-Germanic *uberi (source also of Old Saxon obar, Old Frisian over, Old Norse yfir, Old High German ubar, German über, Gothic ufar "over, above"), from PIE root *uper "over."

As an adjective from Old English uffera. The senses of "past, done,  finished; through the whole extent, from beginning to end" are attested from late 14c. The sense of "so as to cover the whole surface" is from c. 1400. Meaning "leaning forward and down" is from 1540s. The meaning "recovered from" is from 1929. In radio communication, it is used to indicate the speaker has finished speaking (1926).

Above expresses greater elevation, but not necessarily in or near a perpendicular direction; over expresses perpendicularity or something near it: thus, one cloud may be above another, without being over it. Over often implies motion or extension where above would not; hence the difference in sense of the flying of a bird over or above a house, the hanging of a branch over or above a wall. In such uses over seems to represent greater nearness. [Century Dictionary]

Phrase over and above (mid-15c.) is pleonastic, for emphasis. Adjective phrase over-the-counter is attested from 1875, originally of stocks and shares. To be (someone) all over "be exactly what one expects of (someone)" is by 1721.