The verb 'relieve' is another etymological false friend of the '-ceive' word family. While its '-ieve' ending makes it appear related to 'receive,' 'perceive,' and 'conceive,' it derives from a completely different Latin root: 'levāre' (to lift), from 'levis' (light in weight), rather than 'capere' (to take, seize). The convergence of endings is a product of Old French phonology, not shared ancestry.
Latin 'relevāre' combined 're-' (again, back) with 'levāre' (to lift, raise), producing a literal meaning of 'to lift up again' or 'to raise back up.' The metaphorical extension to 'alleviate' or 'lighten a burden' developed naturally: to relieve someone is to lift a weight from them. In military Latin, 'relevāre' acquired the specific sense of replacing a sentinel or garrison, which survives in the English military usage of 'relieving' a guard or 'relieving' a besieged city.
The word entered Middle English around 1350 from Old French 'relever,' which had a broader semantic range than the modern English word. Old French 'relever' meant 'to raise up,' 'to pick up again,' 'to restore,' and 'to relieve.' Modern French preserves this breadth — 'relever' can mean to raise, to note, to relieve, to season (food), or to pick oneself up after a fall. English narrowed the meaning primarily to alleviation and replacement.
The Latin root 'levis' (light in weight) descends from PIE *h₁lengʷʰ- and produced an enormous family in English: 'lever' (a device for lifting), 'levity' (lightness, both literal and figurative), 'elevate' (to lift up), 'alleviate' (to make lighter), and 'levitate' (to rise in the air). More surprisingly, 'carnival' may be related through Late Latin 'carnelevāre' (to remove meat, i.e., the beginning of Lent), though this etymology is debated.
The noun 'relief' entered English from Old French 'relief' and has developed a remarkable range of meanings. In sculpture, 'relief' (from Italian 'rilievo') describes figures that are 'raised' from a flat background — bas-relief, high relief. In geography, 'relief' describes the elevation variations of terrain. In law, 'relief' means the redress sought in a legal action. In baseball, a 'relief pitcher' replaces another. All these senses connect back
The relationship between 'relieve' and 'relevant' is particularly illuminating. 'Relevant' comes from the present participle of Latin 'relevāre' — something 'relevant' is literally something that 'lifts up' or 'raises' the matter under discussion, bearing upon it in a way that lightens the burden of understanding. This etymological connection, invisible to most English speakers, reveals that relevance was originally conceived as a form of assistance — information that helps by lifting the weight of ignorance.