From Latin 'languere' (to be faint) — evolved from physical weakness to the emotional sense of pining in neglect.
To lose or lack vitality; to grow weak or feeble; to suffer from being forced to remain in an unpleasant situation.
From Old French 'languiss-', extended stem of 'languir' (to languish), from Latin 'languere' (to be faint, to be languid, to be weary), from PIE *sleng- (to be slack, to droop) or related to *leg- (to be languid, to lag). Latin 'languere' produced 'languor' (faintness, lassitude), 'languidus' (faint, sluggish), and related 'laxus' (loose, slack) via the root *lag-. The word entered Middle English
In Romantic-era literature, 'languishing' became almost fashionable — poets and novelists portrayed pale, weakened heroes and heroines as aesthetically superior to the vigorous and healthy, turning a word for sickness into an emblem of refined sensibility.