"to cover the surface of (something)," c. 1300, in part from Old English oferlecgan "to place over," also "to overburden," and in part from over- + lay (v.). There also was an overlie in Middle English, but it merged into this word. Similar compounds are found in other Germanic languages, such as German überlegen, Dutch overlegen, Gothic ufarlagjan. Related: Overlaid; overlaying.
in the printing sense, "bit of paper cut and pasted on an impression surface," by 1818, from overlay (v.). Meaning "transparent sheet over a map, chart, etc." is from 1938. In earliest noun use it meant "a necktie" (1725).