Old English full "containing all that can be received; having eaten or drunk to repletion; filled; perfect, entire, utter," from Proto-Germanic *fullaz "full" (source also of Old Saxon full, Old Frisian ful, Dutch vol, Old High German fol, German voll, Old Norse fullr, Gothic fulls), from PIE root *pele- (1) "to fill." Related: Fuller; fullest.
The adverb is Old English ful "very, fully, entirely, completely" and was common in Middle English (full well, full many, etc.); sense of "quite, exactly, precisely" is from 1580s. Full moon, one with its whole disc illuminated, was Old English fulles monan; first record of full-blood in reference to racial purity is from 1812. Full house is 1710 in the theatrical sense, 1887 in the poker sense (three of a kind and a pair, earlier full-hand, 1850). Full-dress (adj.) "appropriate to a formal occasion" is from 1761, from the noun phrase.
Old English hwit "bright, radiant; clear, fair," also as a noun (see separate entry), from Proto-Germanic *hweit- (source also of Old Saxon and Old Frisian hwit, Old Norse hvitr, Dutch wit, Old High German hwiz, German weiß, Gothic hveits), from PIE *kweid-o-, suffixed form of root *kweit- "white; to shine" (source also of Sanskrit svetah "white;" Old Church Slavonic sviteti "to shine," svetu "light;" Lithuanian šviesti "to shine," švaityti "to brighten").
As a surname, originally with reference to fair hair or complexion, it is one of the oldest in English, being well-established before the Conquest. Meaning "morally pure" was in Old English. Association with royalist causes is late 18c. Slang sense of "honorable, fair" is 1877, American English; in Middle English it meant "gracious, friendly, favorable." The racial sense "of those races (chiefly European or of European extraction) characterized by light complexion" is recorded from c. 1600; meaning "characteristic of or pertaining to white people" is from 1852, American English. White supremacy attested from 1868, American English [John H. Van Evrie, M.D., "White Supremacy and Negro Subordination," New York, 1868]; white flight is from 1966, American English.
White way "brightly illuminated street in a big city" is from 1908. White flag of truce or surrender is from c. 1600. White lie is attested from 1741. White Christmas is attested from 1847. White House as the name of the U.S. presidential residence is recorded from 1811. White water "river rapids" is recorded from 1580s. White Russian "language of Byelorussia" is recorded from 1850; the mixed drink is from c. 1978. Astronomical white dwarf is from 1924. White witch, one who used the power for good, is from 1620s.