late 14c., of things, "low, not high," from Late Latin bassus "short, low" (see base (adj.)). Meaning "low in social scale or rank" is recorded from late 14c. Of voices and music notes, "low in tone" from mid-15c. (technically, ranging from the E flat below the bass stave to the F above it), infuenced by Italian basso.
late 14c., "alleviation of distress, hunger, sickness, etc; state of being relieved; that which mitigates or removes" (pain, grief, evil, etc.)," from Anglo-French relif, from Old French relief "assistance," literally "a raising, that which is lifted;" from stressed stem of relever (see relieve).
The meaning "aid to impoverished persons" is attested from c. 1400, from 19c. especially of assistance by governments; that of "deliverance of a besieged town" is from c. 1400. The word was used earlier in English as "that which is left over or left behind," also "feudal payment to an overlord made by an heir upon taking possession of an estate" (both c. 1200).
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Harper, D. (n.d.). Etymology of bas-relief. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/bas-relief