Middle English aboute, from Old English abutan (adv., prep.), earlier onbutan "on the outside of; around the circumference of, enveloping; in the vicinity of, near; hither and thither, from place to place," also "with a rotating or spinning motion," in late Old English "near in time, number, degree, etc., approximately;" a compound or contraction of on (see on; also see a- (1)) + be "by" (see by) + utan "outside," from ut (see out (adv.)).
By c. 1300 it had developed senses of "around, in a circular course, round and round; on every side, so as to surround; in every direction;" also "engaged in" (Wist ye not that I must be about my Father's business?), and gradually it forced out Old English ymbe, ymbutan (from PIE root *ambhi- "around") in the sense "round about, in the neighborhood of."
From mid-13c. as "in the matter, in connection with." From early 14c. as "in partial rotation, so as to face in a different direction." From late 14c. as "near at hand, about one's person." "In a circuitous course," hence "on the move" (late 13c.), and in Middle English "be about to do, be busy in preparation for," hence its use as a future participle in (to be) about to "in readiness, intending." Abouts (late 14c.), with adverbial genitive, still found in hereabouts, etc., probably is a northern dialectal form.
To bring about "cause or affect" and to come about "happen" are from late 14c. About face as a military command (short for right about face) is first attested 1861, American English.
"common deck hand, wharf worker," 1868, American English, perhaps from roust + about. But another theory connects it to British dialect rousing "rough, shaggy," a word associated perhaps with rooster. Meanwhile, compare rouseabout "a restless, roaming person" (1746), which seems to have endured in Australian and New Zealand English. With extended senses in U.S., including "circus hand" (1931); "manual laborer on an oil rig" (1948).