mid-13c. (c. 1200 as a surname), skie, sci, skei, "a cloud," from Old Norse sky "cloud," from Proto-Germanic *skeujam "cloud, cloud cover" (source also of Old English sceo (Middle English sceu) "the sky, the heavens," Old Saxon scio "cloud, region of the clouds, sky;" Old High German scuwo, Old English scua, Old Norse skuggi "shadow;" Gothic skuggwa "mirror"), from PIE root *(s)keu- "to cover, conceal."
The meaning "upper regions of the air; region of clouds, wind, and rain; the heavens, the firmament" is attested from c. 1300; it replaced native heofon in this sense (see heaven). In Middle English, the word can still mean both "cloud" and "heaven," as still in the skies (c. 1300), originally "the clouds."
Sky-high "as high as the sky" is from 1812; optimistic phrase the sky's the limit is attested from 1908. Sky-writing is from 1922. Sky-diving "sport or activity of jumping from an aircraft and free-falling before landing by parachute" is attested from 1959 (sky-diver by 1961; sky-dive (v.) by 1965).