all-round 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.

c. 1300 (early 13c. as a surname), "spherical in shape; circular in outline," of persons or animals, "well-fed;" from Anglo-French rounde, Old French roont (12c., Modern French rond), probably originally *redond, from Vulgar Latin *retundus (source also of Provençal redon, Spanish redondo, Old Italian ritondo), from Latin rotundus "like a wheel, circular, round," related to rota "wheel" (see rotary). The French word is the source of Middle Dutch ront (Dutch rond), Middle High German runt (German rund) and similar words in the Germanic languages. 

As an adverb from c. 1300. As a preposition from c. 1600, "so as to make a complete circuit" (as in round the world); 1715 as "throughout, all through" (as in round the clock); by 1743 as "so as to make a turn or partial circuit about" (as in round the corner). In many cases it is a shortened form of around (adv.).

Of numbers from mid-14c., "entire, full, complete, brought to completion," with the notion of symmetry extended to that of completeness. Round number for one only approximately correct, usually expressed in 10s, 100s, etc., is by 1640s. Compare round (v.). Round trip "an outward and return journey" is by 1844, originally of railways. A round-dance (1520s) is one in which the dancers move in a circle or ring. Round heels attested from 1926, in reference to incompetent boxers, 1927 in reference to loose women, implying in either case a tendency to end up flat on one's back.