mid-15c., of fruits, "ripe, complete in natural growth or development," also, of deliberations, etc., "careful, well-considered, thorough," from Latin mātūrus "ripe, timely, early" (see mature (v.)). Of persons, "having fully developed powers of body and mind," c. 1600. The euphemistic sense of "older than usual" is by 1953.
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.
<a href="https://www.etymonline.com/word/maturely">Etymology of maturely by etymonline</a>
Harper, D. (n.d.). Etymology of maturely. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/maturely