Deeply

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Old English dēop (adjective), dīope, dēope (adverb), of Germanic origin; related to Dutch diep and German tief, also to dip.

wiktionary

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From Middle English depely, deplike, deopliche, from Old English dēoplīċe(“deeply”, adverb), from dēoplīc(“deep”), equivalent to deep +‎ -ly.

etymonline

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deeply (adv.)

Old English deoplice "at or to a great depth," used in both literal and figurative senses; see deep (adj.) + -ly (2). Meaning "profoundly, thoroughly" is from c. 1200; that of "with strong feeling, passionately" from c. 1400. Of sighing from 1550s; of drinking from 1690s.