Probably from ago; deserving, comparable or suitable (as if drawing praise) -- due reward, meet, (un-)worthy.

see GREEK ago

a. weighing, having weight; with a genitive having the weight of (weighing as much as) another thing, of like value, worth as much: βῶς ἄξιος, Homer, Iliad 23, 885; with the genitive of price (Winer's Grammar, 206 (194)), as ἄξιος δέκα μνῶν, common in Attic writings; πᾶν τίμιον οὐκ ἄξιον αὐτῆς (σοφίας) ἐστι, Proverbs 3:15; Proverbs 8:11; οὐκ ἐστι σταθμός πᾶς ἄξιος ψυχῆς, Sir. 26:15; οὐκ ἄξια πρός τήν ... δόξαν are of no weight in comparison with the glory, i. e. are not to be put on an equality with the glory, Romans 8:18; cf. Fritzsche at the passage and Winers Grammar, 405 (378); (Buttmann, 340 (292)).

b. befitting, congruous, corresponding, τίνος, to a thing: τῆς μετανοίας, Matthew 3:8; Luke 3:8; Acts 26:20; ἄξια ὧν ἐπράξαμεν, Luke 23:41. ἄξιον ἐστι it is befitting: α. it is meet, 2 Thessalonians 1:3 (4 Macc. 17:8); β. it is worth the while, followed by τοῦ with an accusative and an infinitive, 1 Corinthians 16:4; — (in both senses very common in Greek writings from Homer and Herodotus down, and often with ἐστι omitted).

c. of one who has merited anything, worthy — both in a good reference and a bad; α. in a good sense; with a genitive of the thing: Matthew 10:10; Luke 7:4; (Luke 10:7); Acts 13:46; 1 Timothy 1:15; 1 Timothy 4:9; 1 Timothy 5:18; 1 Timothy 6:1. followed by the aorist infinitive: Luke 15:19, 21; Acts 13:25; Revelation 4:11; Revelation 5:2, 4, 9, 12; followed by ἵνα: John 1:27 (ἵνα λύσω, a construction somewhat rare; cf. Dem. pro cor., p. 279, 9 ἀξιουν, ἵνα βοηθήσῃ ((dubious); see under the word ἵνα, II. 2 at the beginning and c.)); followed by ὅς with a finite verb (like Latindignus,qui): Luke 7:4 (Buttmann, 229 (198)). It stands alone, but so that the context makes it plain of what one is said to be worthy: Matthew 10:11 (to lodge with); Matthew 10:13 (namely, τῆς εἰρήνης); Matthew 22:8 (namely, of the favor of an invitation); Revelation 3:4 (namely, to walk with me, clothed in white), with a genitive of the person — worthy of one's fellowship, and of the blessings connected with it: Matthew 10:37; Hebrews 11:38 (τοῦ θεοῦ, Sap. iii. 5; Ignatius ad Eph. 2 [ET]). β. in a bad sense; with a genitive of the thing: πληγῶν, Luke 12:48; θανάτου, Luke 23:15; Acts (Acts 23:29); (); ; Romans 1:32; absolutely: Revelation 16:6 (namely, to drink blood).