I have been involved in discussions of the meaning of aion and aionios on this forum for more than 1.5 decades. . Here is something I have researched in the NT.
In the following twenty two verses αἰών and αἰώνιος are defined/described by other words and phrases as eternal, everlasting etc.: 1 Timothy 1:17, 2 Corinthians 4:17-18, 2 Corinthians 5:1, Hebrews 7:24, 1 Peter 1:23, 1 Timothy 6:16, Galatians 6:8, John 6:58, John 10:20, 1 John 2:17, 1 Peter 5:10, Romans 2:7, Luke 1:33, Revelation 14:11, John 10:28, John 3:15, John 3:16, John 5:24, Ephesians 3:21, Romans 20:1, Romans 26:10.
In the NT “aion/aionios” are used to refer to things which are not eternal but are never defined/described as meaning a period of time less than eternal as in the following verses.
[1]1 Timothy 1:17.
(17) Now unto the King eternal, [αἰών/aion] immortal, [ ̓́αφθαρτος/aphthartos] invisible, the only wise God, be honour and glory for ever [αἰών/aion] and ever [αἰώνιος/aionios]. Amen.
In this verse “aion” is paired with “immortal.” “Aion” cannot mean “age(s),” a finite period and be immortal at the same time. Thus “aion” by definition here means “eternal.”
[2]2 Corinthians 4:17-18
(17) For our light affliction, which is but for a moment, worketh for us a far more exceeding and eternal [αἰώνιος/aionios] weight of glory;
(18) While we look not at the things which are seen, but at the things which are not seen: for the things which are seen are temporal;[πρόσκαιρος/proskairos] but the things which are not seen are eternal [αἰώνιος/aionios]
In this passage “aionios” is contrasted with “for a moment,” vs. 4, and “temporal,” vs. 5. “Age(s)” a finite period, it is not the opposite of “for a moment”/”temporal/temporary.” “Eternal” is. See Robertson below. “Aionios” by definition here means “eternal.”
[3]2 Corinthians 5:1
(1)For we know that if our earthly house of this tabernacle were dissolved, we have a building of God, an house not made with hands, eternal [αἰώνιος/aionios] in the heavens.
In this verse “aionios house” is contrasted with “earthly house which is destroyed.” If an “aionios” house is at some time destroyed then it is no different than the earthly house. The aionios house is not destroyed, the opposite of “is destroyed.” Thus “aionios” by definition here means “eternal.” If the tabernacle in heaven is destroyed, it is no different than the earthly tabernacle.
[4]Hebrews 7:24 but because Jesus lives forever [αἰών/aion] he has a permanent [ἀπαράβατος/aparabatos] priesthood.
In this verse “aion” is paired with “unchangeable.” If “aion” means “age(s),” Jesus cannot continue “for a finite period” and be “unchangeable” at the same time. Thus “aion” by definition here means “eternal.”
[5]1 Peter 1:23
(23) For you have been born again, not of perishable seed, but of imperishable, [ ̓́αφθαρτος/aphthartos] through the living and enduring word of God.
1 Peter 1:25
(25) but the word of the Lord endures forever.[αἰών/aion] " And this is the word that was preached to you.
In verse 23 “word of God” is paired with “incorruptible.” In verse 25 the word of God “endures εις τον αιωνα unto eternity. ” Thus by definition “aion” here means “eternity.”
[6]1 Timothy 6:16
(16) Who only hath immortality, [ ̓́αφθαρτος/aphthartos] dwelling in the light which no man can approach unto; whom no man hath seen, nor can see: to whom be honour and power everlasting[αἰώνιος/aionios]
In this verse “aionios” is paired with “immortality.” If “aionios” is only a finite period, God cannot be “immortal” and only exist for a finite period at the same time. Thus “aionios” by definition means “eternal.”
[7]Galatians 6:8
(8) For he that soweth to his flesh shall of the flesh reap corruption;[φθορά/fthora] but he that soweth to the Spirit shall of the Spirit reap life everlasting. [αἰώνιος/aionios]
In this verse “aionios” is contrasted with “corruption.” “Fleshly” people reap “corruption” but spiritual people reap “life aionios,” i.e. not “corruption.” “Age(s) is not opposite of “corruption.” Thus “aionios” by definition here means “eternal/everlasting.”
[8]John 6:58
(58) This is the bread that came down from heaven. Your ancestors ate manna and died, but whoever feeds on this bread will live forever.[αἰώνιος/aionios]
In this verse “aionios life” is contrasted with “death.” If “aionios” is only a finite period, a finite period is not opposite “death.” Thus “aionios” by definition here means “eternal.”
[9]John 10:28
(28) I give them eternal [αἰώνιος/aionios] life, and they shall never [αἰών/aion] perish; no one will snatch them out of my hand.
Here “aionios” and “aion” are paired with not “snatch them out of my hand” If “aion/aionios” means “age(s)” that is not the opposite of “not ‘snatch them out of my hand’” “Aionios” by definition here means “eternal.”
[10]1 John 2:17
(17) The world and its desires pass away, but whoever does the will of God lives forever. [αἰών/aion]
In this verse “aionios” is contrasted with “pass away” “aionios” cannot mean a finite period, A “finite period” is not opposite of “pass away.” Thus “aionios” by definition here means “eternal.”
[11]1 Peter 5:10
(10) And the God of all grace, who called you to his eternal [αιωνιον/aionion] glory in Christ, after you have suffered a little while, [ολιγον/oligon] will himself restore you and make you strong, firm and steadfast.
In this verse “aionios” is contrasted with “little while” “aionios” cannot mean a finite period, A “finite period” is not opposite of “little while.” Thus by definition “aionios” here means “eternal.”
[12]Romans 2:7
(7) To those who by persistence in doing good seek glory, honor and immortality, [ἀφθαρσία/apftharsia] he will give eternal [αἰώνιος/aionios] life.
In this verse “aion” is paired with “immortality.” If “aion” is only a finite period, believers cannot seek for “a finite period,” and “immortality” at the same time. But they can seek for “eternal life” and “immortality” at the same time. Thus by definition “aion” here means “eternal.”
[13]Luke 1:33
(33) And he shall reign over the house of Jacob for ever; [αιωνας/aionas] and of his kingdom there shall be no end.[τελος/τελος]
In this verse “aionios” is paired with “without end.” “aionios” cannot be paired with “without end” if it means only “ages” a finite period. “Aionios” by definition here means eternal.
[14]Revelation 14:11
(11) And the smoke of their torment ascendeth up for ever and ever:[εις αιωνας αιωνων/eis aionas aionas] and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name.
In this verse “aionas aionon torment” is paired with “no rest day or night.” If “aionas, aionon” means “a finite period” at some time they would rest, “Aionas, aionon” by definition here means “forever and forever.”
[15]John 10:28
(28) And I give unto them eternal [αιωνιον] life; and they shall never [εις τον αιωνα] perish, neither shall any man pluck them out of my hand.
In this verse “aionion” is paired with “[no man can] “pluck them out of my hand.” If “aionion” is only a finite period then at some time they could be plucked out. “Aionion” by definition here means eternal.
[16]John 3:15
(15) That whosoever believeth in him should not perish, but have eternal [αιωνιον] life.
In this verse “aionion” is paired with “shall not perish.” They could perish in a finite period, “aionion” by definition here means eternal.
[17]John 3:16
(16) For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting [αιωνιον] life.
In this verse “aionion” is paired with “shall not perish.” They could perish in a finite period, “aionion” by definition here means eternal.
[18]John 5:24
(24) Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting [αἰώνιος] life, and shall not come into condemnation; but is passed from death unto life.
In this verse “aionios” is paired with “shall not come into condemnation” and “passed from life unto death.” “Aionios” does not mean “a finite period,” by definition here it means “eternal.”
[19]Romans 5:21
(21) That as sin hath reigned unto death, even so might grace reign through righteousness unto eternal [αἰώνιος] life by Jesus Christ our Lord.
In this verse “aionios” is contrasted with death. “A finite period” is not opposite death, “eternal life” is. “Aionios” by definition here means ‘eternal.”
[20]Ephesians 3:21
(21) to him be glory in the church and in Christ Jesus throughout all generations, for ever [του αιωνος/tou aionios] and ever! [των αιωνων/ton aionion] Amen.
In this verse “tou aionios ton aionion” is paired with “throughout all generations.” "Age(s)" a finite period cannot refer to "all generations."
[21]Romans 1:20
(20) For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal [ἀΐ́διος] power and Godhead; so that they are without excuse:
[22]Romans 16:26
(26) But now is made manifest, and by the scriptures of the prophets, according to the commandment of the everlasting [αἰώνιος] God, made known to all nations for the obedience of faith:
In Romans 1:20 Paul refers to God’s power and Godhead as “aidios.” Scholars agree “aidios” unquestionably means eternal, everlasting, unending etc. In Rom 16:26 Paul refers to God as “aionios,” therefore Paul considers “aidios” and “aionios” to be synonymous.
=======
• A. T. Robertson, Word Pictures in the New Testament 2 Co 4:17
(17) For our light affliction, which is but for a moment, worketh for us a far more exceeding and eternal weight of glory;
Literally, “the for the moment (old adverb parautika, here only in N.T.) lightness (old word, in N.T. only here and Mat_11:30).”
More and more exceedingly (kath' huperbolēn eis huperbolēn). Like piling Pelion on Ossa, “according to excess unto excess.” See note on 1Co 12:31.
Eternal weight of glory (aiōnion baros doxēs). Careful balancing of words in contrast (affliction vs. glory, lightness vs. weight, for the moment vs. eternal).
• Vincent Word Studies in the New Testament
A far more exceeding and eternal weight of glory (καθ' ὑπερεβολὴν εἰς ὑπερβολὴν αἰώνιον βάρος δόξης)
Rev., more and more exceedingly an eternal weight, etc. An expression after the form of Hebrew superlatives, in which the emphatic word is twice repeated. Lit., exceedingly unto excess. The use of such cumulative expressions is common with Paul. See, for example, Phi 1:23, lit., much more better; Rom 8:37, abundantly the conquerors; Eph 3:20, exceeding abundantly, etc. Note how the words are offset: for a moment, eternal; light, weight; affliction, glory.
Vincent Ephesians 3:21
(21) to him be glory in the church and in Christ Jesus throughout all generations, for ever and ever! Amen.
Glory Properly, the glory, which is His due.
In the Church
Through which His many-tinted wisdom is to be displayed, and which is His fullness. The variety of the divine wisdom is again hinted at in all that we ask or think.
By Christ Jesus (ἐν)
Rev., better, in. As the Church is the outward domain in which God is to be praised, so Christ is the spiritual sphere of this praise.
Throughout all ages, world without end (εἰς πάσας τὰς γενεὰς τοῦ αἰῶνος τῶν αἰώνων)
Lit., unto all the generations of the age of the ages. Eternity is made up of ages, and ages of generations.
