"irritably," 1730; earlier "adversely, unfavorably," also "athwart, intersecting something else" (both 1590s), from cross (adj.) + -ly (2).
Entries linking to crossly
cross adj.
1520s, in part a shortening of across, in part from the adverb (see cross (adv.)). Earliest sense is "falling athwart, lying athwart the main direction, passing from side to side." Meaning "intersecting, lying athwart each other" is from c. 1600.
Sense of "adverse, opposed, obstructing, contrary, opposite" is from 1560s; of persons, "peevish, ill-tempered," from 1630s, probably from the earlier senses of "contrary, athwart," especially with reference to winds and sailing ships. A 19c. emphatic form was cross as two sticks (1807), punning on the verb. Cross-grained is from 1670s of wood; as "opposed in nature or temper" from 1640s.
-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.