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.
It is reconstructed to be 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").
It was productive as a prefix in Old English, as in German and Scandinavian (often forming words modeled on Latin ones in sub-); Middle English had more than 200 words with it.
The 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 a different root; compare understand).
In many figurative expressions: 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 get something under (one's) belt was literally to eat or drink it (1839), figurative use is by 1931. To be under (someone's) wing "protected by (someone)" is recorded from early 13c.
To speak under (one's) breath "in a low voice" is attested by 1832.