mid-15c., "relative, having relation or reference to something" (a sense now obsolete), from Medieval Latin respectivus "having regard for," from Latin respect- past-participle stem of respicere "look back at, regard, consider" (see respect (v.)). The meaning "relating or pertaining severally each to each, connected with each of those in question" is from 1640s.
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.
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Harper, D. (n.d.). Etymology of respectively. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/respectively