"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 Gothic ufarlagjan. Related: Overlaid; overlaying.

in the printing sense, 1824, from overlay, v.. Meaning "transparent sheet over a map, chart, etc." is from 1938. In earliest noun use it meant "a necktie" (1725).