justly adv.

late 14c., "morally upright, righteous  in the eyes of God" ("Now chiefly as a Biblical archaism" - OED); also "equitable, fair, impartial in one's dealings;" also "fitting, proper, conforming to standards or rules;" also "justifiable, reasonable;" from Old French juste "just, righteous; sincere" (12c.) and directly from Latin iustus "upright, righteous, equitable; in accordance with law, lawful; true, proper; perfect, complete" (source also of Spanish and Portuguese justo, Italian giusto), from ius "a right," especially "legal right, law" (see jurist; from Latin ius also come English jury (n.), injury, etc.).

From c. 1400 as "right-minded, good in intention;" from early 15c. as "legal, lawful, right in law." Also "exact, precise; marked or characterized by precision; having correct dimensions" (late 14c.); of narrations, calculations, etc., "accurate, correct" (early 15c.). The sense in music, "harmonically pure, correct, and exact" is by 1850.

The more mundane Latin law-word lex covered specific laws as opposed to the body of laws. The noun meaning "righteous person or persons; Christ" is from late 14c. (The neuter adjective in Latin was used as a noun, iustum, "what is right or just").

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.