late 14c., "morally upright, righteous in the eyes of God; justifiable; equitable, impartial, fair; conforming to rules," also "marked or characterized by precision; exact, having correct dimensions," from Old French juste "just, righteous; sincere" (12c.), from Latin iustus "upright, righteous, equitable; in accordance with law, lawful; true, proper; perfect, complete," from ius "a right," especially "legal right, law" (see jurist). The more mundane Latin law-word lex covered specific laws as opposed to the body of laws. The noun meaning "righteous person or persons" is from late 14c.
"merely, barely," 1660s, from Middle English sense of "exactly, precisely, punctually" (c. 1400), from just (adj.), and paralleling the adverbial use of French juste. Just now "a short time ago" is from 1680s. For sense decay, compare anon, soon. Just-so story first attested 1902 in Kipling, from the expression just so "exactly that, in that very way" (1751).