Etymology
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skin (v.)

late 14c., skinnen, "to remove the skin from" (originally in reference to circumcision), from skin (n.). As "to have (a particular kind of) skin" from c. 1400. As "provide with skin, cover as with skin," 1540s.

In 19c. U.S. colloquial use, "to strip of valuable possessions, fleece, plunder;" hence skin-game (1868), one in which one player has no chance against the others (as with a stacked deck), the type of con game played in a skin-house ("gambling house;" the same phrase, for "theater featuring nude women" is attested by 1972). Skin the cat in gymnastics is from 1845. Related: Skinned; skinning.

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over- 

word-forming element meaning variously "above; highest; across; higher in power or authority; too much; above normal; outer; beyond in time, too long," from Old English ofer (from PIE root *uper "over"). Over and its Germanic relations were widely used as prefixes, and sometimes could be used with negative force. This is rare in Modern English, but compare Gothic ufarmunnon "to forget," ufar-swaran "to swear falsely;" Old English ofercræft "fraud."

In some of its uses, moreover, over is a movable element, which can be prefixed at will to almost any verb or adjective of suitable sense, as freely as an adjective can be placed before a substantive or an adverb before an adjective. [OED]

Among the old words not now existing are Old English oferlufu (Middle English oferlufe), literally "over-love," hence "excessive or immoderate love." Over- in Middle English also could carry a sense of "too little, below normal," as in over-lyght "of too little weight" (c. 1400), overlitel "too small" (mid-14c.), oversmall (mid-13c.), overshort, etc.

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skin (n.)

c. 1200, "animal hide" (usually dressed and tanned), from Old Norse skinn "animal hide, fur," from Proto-Germanic *skinth- (source also of rare Old English scinn, Old High German scinten, German schinden "to flay, skin;" German dialectal schind "skin of a fruit," Flemish schinde "bark"), from PIE *sken- "to peel off, flay" (source also of Breton scant "scale of a fish," Irish scainim "I tear, I burst"), extended form of root *sek- "to cut."

The usual Anglo-Saxon word is hide (n.1). The meaning "epidermis of a living animal or person" is attested from early 14c.; extended to fruits, vegetables, etc. late 14c. Jazz slang sense of "drum" is from 1927. As short for skinhead from 1970. As an adjective, it formerly had a slang sense of "cheating" (1868, compare the verb); that of "pornographic" is attested from 1968. Skin deep "superficial, not deeper than the thickness of the skin" (also literally, of wounds, etc.) is attested by 1610s:

All the carnall beauty of my wife, Is but skin-deep.
[Sir Thomas Overbury, "A Wife," 1613; the poem was a main motive for his murder]

The skin of one's teeth as the narrowest of margins is attested from 1550s in the Geneva Bible, a literal translation of the Hebrew text in Job xix.20. To get under (someone's) skin "annoy" is from 1896. Skin graft is from 1871. Skin merchant "recruiting officer" is from 1792 (the older sense is "dealer in hides"). Skin and bone as a description of emaciation or extreme leanness is in Middle English:

Ful of fleissche Y was to fele, Now ... Me is lefte But skyn & boon. [hymn, c. 1430]
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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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walk-over (n.)

"easy victory," 1838, such as one that happens in the absence of competitors, when the solitary starter, being obliged to complete the event, can traverse the course at a walk. Transferred sense of "anything accomplished with great ease" is attested from 1902. To walk (all) over (someone) "treat with contempt" is from 1851.

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cross-over (n.)

also crossover, 1795, a term in calico-printing, "superimposed color in the form of stripes or crossbars," from the verbal phrase; see cross (v.) + over (adv.). From 1884 in railroading; from 1912 in biology. As a general adjective from 1893; specifically of musicians and genres from 1971.

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fly-over (n.)

also flyover, 1901 of bridges, 1931, of aircraft flights, from fly (v.1) + over (adv.).

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sleep-over (n.)

"a spending of a night in a place other than one's residence," 1935, from the verbal phrase; see sleep (v.) + over (adv.). Earlier the verbal phrase meant "sleep late, oversleep" (1827).

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eel-skin (n.)

1560s, from eel + skin (n.). "Formerly used as a casing for the cue or pigtail of the hair or the wig, especially by sailors." [Century Dictionary]

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skin-diver (n.)

"one who goes underwater without a full diving suit," 1932, from skin (n.) + diver (n.). Related: Skin-diving.

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