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c.1400, "to buy up the whole stock of" (in Anglo-French from c.1300), from Old French en gros "in bulk, in a large quantity, at wholesale," as opposed to en detail. See gross.
Figurative sense of "absorb the whole attention" is first attested 1709. A parallel engross, meaning "to write (something) in large letters," is from Anglo-French engrosser, from Old French en gros "in large (letters)." Related: Engrossed; engrossing.