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1723, a Kentish word of unknown origin. Originally a piece of iron fitted to a plow for scraping soil; meaning "thin slip of wood to fill up a space or raise a level" is from 1860.
"to wedge up a surface by means of a shim," 1877, from shim (n.). Related: Shimmed; shimming.
To vacillate; be irresolute: For god sake, stop shilly-shallying and make up your mind
[1782+; found by 1700 in form shill I shall I]