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.

Definitions of over
over (adv.)
at or to a point across intervening space etc.;
come over and see us some time
over there
over (adv.)
throughout an area;
he is known the world over
over (adv.)
throughout a period of time;
stay over the weekend
Synonyms: o'er
over (adv.)
beyond the top or upper surface or edge; forward from an upright position;
a roof that hangs over
over (adv.)
over the entire area;
she ached all over
everything was dusted over with a fine layer of soot
Synonyms: all over
over (n.)
(cricket) the division of play during which six balls are bowled at the batsman by one player from the other team from the same end of the pitch;
over (adj.)
having come or been brought to a conclusion;
the affair is over, ended, finished
Synonyms: complete / concluded / ended / all over / terminated