big:  Big is one of the notorious mystery words of English etymology – extremely common in the modern language, but of highly dubious origin. In its earliest use in English it meant ‘powerful, strong’, and it is not really until the 16th century that we get unequivocal examples of it in the modern sense ‘large’. It occurs originally in northern texts, only slowly spreading south, which suggests that it may be of Scandinavian origin; some have compared Norwegian dialect bugge ‘important man’.
c. 1300, northern England dialect, "powerful, strong," of obscure origin, possibly from a Scandinavian source (compare Norwegian dialectal bugge "great man"). Old English used micel in many of the same senses. Meaning "of great size" is late 14c.; that of "grown up" is attested from 1550s. Sense of "important" is from 1570s. Meaning "generous" is U.S. colloquial by 1913.
Big band as a musical style is from 1926. Slang big head "conceit" is first recorded 1850. Big business "large commercial firms collectively" is 1905; big house "penitentiary" is U.S. underworld slang first attested 1915 (in London, "a workhouse," 1851). In financial journalism, big ticket items so called from 1956. Big lie is from Hitler's grosse Lüge.