Perhaps from eu and tithemi; straight, i.e. (literally) level, or (figuratively) true; adverbially (of time) at once -- anon, by and by, forthwith, immediately, straightway.
see GREEK eu
see GREEK tithemi
a. properly, straight, level: of a way (Matthew 3:3); Mark 1:3; Luke 3:4; Acts 9:11; εἰς εὐθεῖαν (L T Tr WH εἰς εὐθείας), namely, ὁδόν (an ellipsis common also in classical Greek cf. Winer's Grammar, § 64, 5), Luke 3:5; εὐθεῖα ὁδός the straight, the right way, is figuratively used of true religion as a rule of life leading to its goal, i. e. to salvation, 2 Peter 2:15; αἱ ὁδοί κυρίου, the right and saving purposes of God, Acts 13:10 (Song of the Three Children, verse 3).
b. tropically, straightforward, upright, true, sincere (as often in secular authors): καρδία, Acts 8:21 (εὐθεῖς τῇ καρδία often in the Psalms, as Psalm 7:11; Psalm 31:11 STRONGS NT 2117: εὐθύς (adv)εὐθύς (adv), adverb (from Pindar down), equivalent to εὐθέως, with which it is often interchanged in the manuscripts (see εὐθέως); straightway, immediately, forthwith: Matthew 3:16; Matthew 13:20; John 13:32, etc. (Cf. Phryn. ed. Lob., p. 145.)