mildly adv.

Old English milde, of persons, powers, or dispositions, "possessing softness or gentleness, good-tempered, merciful," from Proto-Germanic *milthjaz- (source also of Old Norse mildr (which also contributed to the English word), Old Saxon mildi, Old Frisian milde, Middle Dutch milde, Dutch mild, Old High German milti, German milde "mild," Gothic mildiþa "kindness"), from PIE *meldh-, from root *mel- (1) "soft," which is the source also of Latin mollis "soft."

Of weather, "not rough or stormy," late 14c. Of medicine, etc., "gentle or moderate in force, operation, or effect," c. 1400; of disease from 1744. Of rule, punishment, etc., "moderate in quality or degree, of mitigated force, not hard to endure," by 1570s. It was also used in Old English as an adverb, meaning "mercifully, graciously."

Mild goes further than gentle in expressing softness of nature; it is chiefly a word of nature or character, while gentle is chiefly a word of action. [Century Dictionary]

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.