Perhaps from a (as a negative particle) and the base of meros; properly, to miss the mark (and so not share in the prize), i.e. (figuratively) to err, especially (morally) to sin -- for your faults, offend, sin, trespass.
see GREEK a
see GREEK meros
a. absolutely: Matthew 27:4; John 5:14; John 8:11; John 9:2; 1 John 1:10; 1 John 2:1; 1 John 3:6, 8; 1 John 5:18; Romans 2:12; Romans 3:23; Romans 5:12, 14, 16; Romans 6:15; 1 Corinthians 7:28, 36; 1 Corinthians 15:34; Ephesians 4:26; 1 Timothy 5:20; Titus 3:11; Hebrews 3:17; Hebrews 10:26 (ἑκουσίως); (2 Peter 2:4); of the violation of civil laws, which Christians regard as also the transgression of divine law, 1 Peter 2:20.
b. ἁμαρτάνειν ἁμαρτίαν to commit (literally, sin) a sin, 1 John 5:16 (μεγάλην ἁμαρτίαν, Exodus 32:30f. Hebrew חֲטָאָה חָטָא; αἰσχρὰν ἁμαρτάνω Sophocles Phil. 1249; μεγάλα ἁμαρτήματα ἁμαρτάνειν, Plato, Phaedo, p. 113 e.); cf. ἀγαπάω, under the end ἁμαρτάνειν εἰς τινα (Buttmann, 173 (150); Winer's Grammar, 233 (219)): Matthew 18:15 (L T WH omit; Tr marginal reading brackets εἰς σε), Matthew 18:21; Luke 15:18, 21; Luke 17:3 Rec., 4; 1 Corinthians 8:12; τί εἰς Καίσαρα, Acts 25:8; εἰς τό ἴδιον σῶμα, 1 Corinthians 6:18 (εἰς αὑτούς τέ καί εἰς ἄλλους, Plato, rep. 3, p. 396 a.; εἰς τό θεῖον, Plato, Phaedr., p. 242 c.; εἰς Θεούς, Xenophon, Hell. 1, 7, 19, etc.; (cf. ἁμαρτάνω κυρίῳ Θεῷ, Baruch 1:13 Baruch 2:5)); Hebraistically, ἐνώπιον (לִפְּנֵי) τίνος (Buttmann, § 146, 1) in the presence of, before anyone, the one wronged by the sinful act being, as it were, present and looking on: Luke 15:18, 21 (1 Samuel 7:6; Tobit 3:3, etc.; (cf. ἔναντι κυρίου, Baruch 1:17)). (For references see ἁμαρτία. Compare: προαμαρτάνω).