daylight n.

Old English dæg "period during which the sun is above the horizon," also "lifetime, definite time of existence," from Proto-Germanic *dages- "day" (source also of Old Saxon, Middle Dutch, Dutch dag, Old Frisian di, dei, Old High German tag, German Tag, Old Norse dagr, Gothic dags), according to Watkins, from PIE root *agh- "a day."  He adds that the Germanic initial d- is "of obscure origin." But Boutkan says it is from PIE root *dhegh- "to burn" (see fever). Not considered to be related to Latin dies (which is from PIE root *dyeu- "to shine").

Meaning originally, in English, "the daylight hours;" it expanded to mean "the 24-hour period" in late Anglo-Saxon times. The day formerly began at sunset, hence Old English Wodnesniht was what we would call "Tuesday night." Names of the weekdays were not regularly capitalized in English until 17c.

From late 12c. as "a time period as distinguished from other time periods." Day-by-day "daily" is from late 14c.; all day "all the time" is from late 14c.  Day off "day away from work" is attested from 1883; day-tripper first recorded 1897. The days in nowadays, etc. is a relic of the Old English and Middle English use of the adverbial genitive.

All in a day's work "something unusual taken as routine" is by 1820. The nostalgic those were the days is attested by 1907. That'll be the day, expressing mild doubt following some boast or claim, is by 1941. To call it a day "stop working" is by 1919; earlier call it a half-day (1838). One of these days "at some day in the near future" is from late 15c. One of those days "a day of misfortune" is by 1936.

"brightness, radiant energy, that which makes things visible," Old English leht (Anglian), leoht (West Saxon), "light, daylight; spiritual illumination," from Proto-Germanic *leukhtam (source also of Old Saxon lioht, Old Frisian liacht, Middle Dutch lucht, Dutch licht, Old High German lioht, German Licht, Gothic liuhaþ "light"), from PIE root *leuk- "light, brightness."

The -gh- was an Anglo-French scribal attempt to render the Germanic hard -h- sound, which has since disappeared from this word. The figurative spiritual sense was in Old English; the sense of "mental illumination" is first recorded mid-15c. Meaning "something used for igniting" is from 1680s. Meaning "a consideration which puts something in a certain view" (as in in light of) is from 1680s. Short for traffic light from 1938. Quaker use is by 1650s; New Light/Old Light in church doctrine also is from 1650s. Meaning "person eminent or conspicuous" is from 1590s. A source of joy or delight has been the light of (someone's) eyes since Old English:

Ðu eart dohtor min, minra eagna leoht [Juliana].

Phrases such as according to (one's) lights "to the best of one's natural or acquired capacities" preserve an older sense attested from 1520s. To figuratively stand in (someone's) light is from late 14c. To see the light "come into the world" is from 1680s; later as "come to full realization" (1812). The rock concert light-show is from 1966. To be out like a light "suddenly or completely unconscious" is from 1934.