To be completely engrossed or overwhelmed. These phrases, likening physical immersion in something to figurative engrossment, have been around a long time. Richard Barnfield used “In love up to the eares” in The Affectionate Shepheard (1594). Anthony Trollope had “All the Burtons are full up to their eyes with good sense” in The Claverings (1866), about a century after the term came into use.