late 14c., religiousli, "piously, devoutly, in a religious manner," from religious + -ly (2). Transferred sense of "exactly, strictly, scrupulously" is attested by 1570s.
Entries linking to religiously
religious adj.
c. 1200, "devout, pious, imbued with or expressive of religious devotion," used of Christians, Jews, pagans; also "belonging to a religious order," from Anglo-French religius, Old French religious (12c., Modern French religieux) and directly from Latin religiosus, "pious, devout, reverencing or fearing the gods," also "religiously careful, anxious, or scrupulous," from religio "religious observance; holiness" (see religion).
The meaning "pertaining to religion" is from 1530s. The transferred sense of "scrupulous, exact, conscientious" is recorded from 1590s but restores or revives a sense right at home among the superstitious Romans. As a noun, from c. 1200 as "persons bound by vow to a religious order;" from late 14c. as "pious persons, the devout." Related: Religiousness.
-ly 2
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.