Old English under (prep.) "beneath, among, before, in the presence of, in subjection to, under the rule of, by means of," also, as an adverb, "beneath, below, underneath," expressing position with reference to that which is above, from Proto-Germanic *under- (source also of Old Frisian under, Dutch onder, Old High German untar, German unter, Old Norse undir, Gothic undar), from PIE *ndher- "under" (source also of Sanskrit adhah "below;" Avestan athara- "lower;" Latin infernus "lower," infra "below").
Productive as a prefix in Old English, as in German and Scandinavian (often forming words modeled on Latin ones in sub-). Notion of "inferior in rank, position, etc." was present in Old English. With reference to standards, "less than in age, price, value," etc., late 14c. As an adjective, "lower in position; lower in rank or degree" from 13c. Also used in Old English as a preposition meaning "between, among," as still in under these circumstances, etc. (though this may be an entirely separate root; see understand).
Under the weather "indisposed" is from 1810. Under the table is from 1913 in the sense of "very drunk," 1940s in sense of "illegal" (under-board "dishonest" is from c. 1600). To keep something under (one's) hat "secret" is from 1885; to have something under (one's) nose "in plain sight" is from 1540s; to speak under (one's) breath "in a low voice" is attested from 1832.
past participle of do (v.); from Old English past participle gedon (a vestige of the prefix is in ado). As a past-participle adjective meaning "completed, finished, performed, accomplished" from early 15c. As a word of acceptance of a deal or wager, 1590s.
U.S. Southern use of done in phrases such as done gone (or "Octopots done got Albert!") is attested by 1827, according to OED: "a perfective auxiliary or with adverbial force in the sense 'already; completely.' " Century Dictionary writes that it was "originally causal after have or had, followed by an object infinitive ; in present use the have or had is often omitted and the infinitive turned into a preterit, leaving done as a mere preterit sign" and calls it "a characteristic of negro idiom."
To be done in "exhausted" is by 1917. Slang done for "doomed" is by 1803 (colloquial do for "ruin, damage" is from 1740). To have done it "to have been very foolish, made a mess of things" is from 1837.