Etymology
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hyper- 
word-forming element meaning "over, above, beyond," and often implying "exceedingly, to excess," from Greek hyper (prep. and adv.) "over, beyond, overmuch, above measure," from PIE root *uper "over."
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surmount (v.)
early 14c., "to rise above, go beyond," from Old French surmonter "rise above," from sur- "beyond" (see sur- (1)) + monter "to go up" (see mount (v.)). Meaning "to prevail over, overcome" is recorded from late 14c. Related: Surmounted; surmounting.
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headroom (n.)
"space above the head," 1851, from head (n.) + room (n.).
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overhead (adv.)

mid-15c., over-hed, "above one's head, aloft," from over- + head (n.) or from a survival of Old English oferheafod. The adjective, "situated above or aloft," is attested from 1874. As a noun, short for overhead costs, etc., it is attested by 1914.

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over (prep., adv.)

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.

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supernatant (adj.)
"floating on the surface," 1660s, from Latin supernatantem (nominative supernatans), present participle of supernatare "to swim above," from super "above, over" (see super-) + natare "to swim," frequentative of nare "to swim" (from PIE root *sna- "to swim"). Related: Supernatation (1620s).
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sur- (1)
word-forming element meaning "over, above, beyond, in addition," especially in words from Anglo-French and Old French, from Old French sour-, sor-, sur-, from Latin super "above, over," from PIE root *uper "over."
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overtop (v.)

"rise above or beyond the top of," 1560s, from over- + top (v.). Related: Overtopped; overtopping.

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overground (adj.)
"situated above ground" (as opposed to underground), 1879, from over- + ground (n.).
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mantelpiece (n.)

"the horizontal shelf or hood above a fireplace," 1680s, from mantel + piece (n.1).

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