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"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, e.g. 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).