Etymology
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lay (adj.)

"uneducated, non-professional; non-clerical," early 14c., from Old French lai "secular, not of the clergy" (12c., Modern French laïque), from Late Latin laicus, from Greek laikos "of the people," from laos "(the common) folk, the people, the crowd; the military; a tribe," in the New Testament especially "the Jewish people," also "the laity," a word of unknown origin. Beekes writes that it is "most often connected with" Hittite lahh- "campaign" and Old Irish laech "warrior," but that the form "is rather Pre-Greek, and has a Pre-Greek suffix -it(o)-. In Middle English, contrasted with learned, a sense revived 1810 in contrast to expert. Laic is a more modern borrowing directly from Late Latin.

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lay (v.)

"to cause to lie or rest," Old English lecgan "to place on the ground (or other surface); place in an orderly fashion," also "put down" (often by striking), from Proto-Germanic *lagojanan (source also of Old Saxon leggian, Old Norse leggja, Old Frisian ledza, Middle Dutch legghan, Dutch leggen, Old High German lecken, German legen, Gothic lagjan "to lay, put, place"), from PIE root *legh- "to lie down, lay." This is the causative form of the ancient Germanic verb that became modern English lie (v.2).

Meaning "have sex with" first recorded 1934, in U.S. slang, probably from sense of "bring forth and deposit" (which was in Old English, as in lay an egg, lay a bet, etc.), perhaps reinforced by to lie with, a phrase frequently met in the Bible. To lay for (someone) "await a chance at revenge" is from late 15c.; lay low "stay inconspicuous" is from 1839; to lay (someone) low "defeat" (late 14c.) preserves the secondary Old English sense.

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lay (n.1)

"short song," mid-13c., from Old French lai "song, lyric," of unknown origin. Perhaps from Celtic (compare Irish laid "song, poem," Gaelic laoidh "poem, verse, play") because the earliest verses so called were Arthurian ballads, but OED finds this "out of the question" and prefers a theory which traces it to a Germanic source, such as Old High German leich "play, melody, song."

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lay (n.2)

1550s, "act of laying," from lay (v.). From 1580s as "a wager." Meaning "relative position, direction, etc.,; way in which something is laid" (as in lay of the land) first recorded 1819. Slang meaning "line of business" is from 1707. Meaning "woman perceived as available for sex" is attested from 1930, but there are suggestions of it in stage puns from as far back as 1767.

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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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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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