all-over adj.

Old English eall "every, entire, the whole quantity of" (adj.), "fully, wholly, entirely" (adv.), from Proto-Germanic *alnaz (source also of Old Frisian, Old High German al; German all, alle; Old Norse allr; Gothic alls), with no certain connection outside Germanic. As a noun, in Old English, "all that is, everything."

Combinations with all meaning "wholly, without limit" were common in Old English (such as eall-halig "all-holy," eall-mihtig "all-mighty") and the habit has continued. Middle English had al-wher "wherever; whenever" (early 14c.); al-soon "as soon as possible," al-what (c. 1300) "all sorts of things, whatever."

Of the common modern phrases with it, at all "in any way" is from mid-14c., and all "and everything (else)" is from 1530s, all but "everything short of" is from 1590s. First record of all out "to one's full powers" is by 1880. All clear as a signal of "no danger" is recorded from 1902. All right, indicative of assent or approval, is attested by 1837; the meaning "satisfactory, acceptable" is by 1939, from the notion of "turning out well."

The use of a, a' as an abbreviation of all (as in Burns' "A Man's a Man for A' that") is a modern Scottishism but has history in English to 13c.

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.