Old English han "a stone, rock, (boundary) stone," from Proto-Germanic *haino (source also of Old Norse hein "hone"), from PIE *ko- "to sharpen, whet." The specific sense "whetstone, stone used for sharpening tools that require a delicate edge" emerged in Middle English (early 14c.). "A hone differs from a whetstone in being of finer grit and more compact texture" [Century Dictionary].
"rub or sharpen on or as on a hone," 1788, from hone (n.). Related: Honed; honing. The verb form in Middle English (hene) and Old English (hænan) meant "cast stones at."