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.
"absent in mind, distracted from present reality by intellectual activity," 1640s, past-participle adjective from abstract (v.). Related: Abstractedly.
An absent man is one whose mind wanders unconsciously from his immediate surroundings, or from the topic which demands his attention; he may be thinking of little or nothing. An abstracted man is kept from what is present by thoughts and feelings so weighty or interesting that they engross his attention. [Century Dictionary]
Old English etan (class V strong verb; past tense æt, past participle eten) "to consume food, devour, consume," from Proto-Germanic *etan (source also of Old Frisian ita, Old Saxon etan, Middle Dutch eten, Dutch eten, Old High German ezzan, German essen, Old Norse eta, Gothic itan), from PIE root *ed- "to eat."
Transferred sense of "corrode, wear away, consume, waste" is from 1550s. Meaning "to preoccupy, engross" (as in what's eating you?) first recorded 1893. Slang sexual sense of "do cunnilingus on" is first recorded 1927. The slang phrase eat one's words "retract, take back what one has uttered" is from 1570s; to eat one's heart out is from 1590s; for eat one's hat, see hat. Eat-in (adj.) in reference to kitchens is from 1955. To eat out "dine away from home" is from 1930.