Justify
Middle English (in the senses ‘administer justice to’ and ‘inflict a judicial penalty on’): from Old French justifier, from Christian Latin justificare ‘do justice to’, from Latin justus (see just).
wiktionary
From Middle English justifien, from Old French justifier, from Late Latin justificare(“make just”), from Latin justus, iustus(“just”) + ficare(“make”), from facere, equivalent to just + -ify.
etymonline
justify (v.)
c. 1300, "to administer justice;" late 14c., "to show (something) to be just or right," from Old French justifiier "submit to court proceedings" (12c.), from Late Latin iustificare "act justly toward; make just," from Latin iustificus "dealing justly, righteous," from iustus "just" (see just (adj.)) + combining form of facere "to make, to do" (from PIE root *dhe- "to set, put").
Meaning "declare to be innocent or blameless" is from 1520s. Of circumstances, "to afford justification," from 1630s. Meaning "to make exact" (now largely restricted to typesetting) is from 1550s. Related: Justified; justifier; justifying.