mid-14c., "furnish with" (goods, provisions, etc.), also "reinforce" (troops), from Old French estofer "pad, upholster, fit out" (Modern French étoffer), from estoffe, and probably also in part from stuff (n.).
From c. 1400 as "fill, cram full; fill (the belly) with food or drink, gorge;" from early 15c. as "to clog" (the sinuses, etc.); from late 14c. as "fill (a mattress, etc.) with padding, line with padding;" also in the cookery sense, in reference to filing the interior of a pastry or the cavity of a fowl or beast. The ballot-box sense is attested from 1854, American English; in expressions of contempt and suggestive of bodily orifices, it dates from 1952.