In a way that shows no hope or expectation of success; beyond hope or remedy.
From 'hopeless' (hope + -less, meaning without hope) plus the adverb suffix '-ly.' The term became common in the 1600s-1700s.
The word 'hopelessly' is paradoxically used to describe things we care about—'hopelessly in love' is actually romantic, not depressing, which shows how context completely changes a word's emotional weight!
Complete word intelligence in one call. Free tier — 50 lookups/day.