"possessed of or endowed with might; having much ability, strength, or power," Old English mihtig, earlier mæhtig, from Proto-Germanic *mahtiga- (source also of Old Frisian mechtig, Old Saxon mahtig, Dutch machtig, German mächtig), from the source of might (n.). As an adverb, "very, exceedingly, greatly," it is attested from c. 1300, though such use now is considered colloquial.
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.
Others are reading
Definitions of mightily
powerfully or vigorously;
he strove mightily to achieve a better position in life
(Southern regional intensive) very; to a great degree;