c. 1300, "having the appearance of truth or fact," perhaps from Old Norse likligr "likely," from likr "like" (see like (adj.)). Old English had cognate geliclic. Meaning "having the appearance of being strong and capable" is from mid-15c., though now mostly confined to American English; according to OED this sense is perhaps influenced by like (v.). Sense of "good-looking" ("such as may be liked") is from late 15c. Meaning "probable" is attested from late 14c., but said by OED to be now principally in American English. As an adverb, late 14c., from the adjective.
LIKELY. That may be liked; that may please; handsome. In the United States, as a colloquial term, respectable; worthy of esteem; sensible.--Worcester. [Bartlett]