Let's go through these quotes one by one and examine them closely:
Dr. R.F. Weymouth, a translator who was adept in Greek, states in The New Testament in Modern Speech (p. 657), "Eternal, Greek aeonian, i.e., of the ages: Etymologically this adjective, like others similarly formed does not signify, "during" but "belonging to" the aeons or ages."
Etymologically it does, but we're not talking about the meaning of the etymological root, we're talking about the word itself.
This quote alone proves that insisting on the meaning 'age' or 'ages' is committing the etymological (or 'root word'), fallacy.
Dr. Marvin Vincent, in his Word Studies of the New Testament (vol. IV, p. 59): "The adjective aionios in like manner carries the idea of time. Neither the noun nor the adjective in themselves carries the sense of "endless" or "everlasting." Aionios means enduring through or pertaining to a period of time. Out of the 150 instances in the LXX (Septuagint), four-fifths imply limited duration."
Firstly, Vincent makes assertions without evidence. Where is the data to support him? Secondly, what is to be done with the other fifth?
Dr. F.W. Farrar, author of The Life of Christ and The Life and Work of St. Paul, as well as books about Greek grammar and syntax, writes in The Eternal Hope (p. 198 ) , "That the adjective is applied to some things which are "endless" does not, of course, for one moment prove that the word itself meant 'endless;' and to introduce this rendering into many passages would be utterly impossible and absurd."
In his book, Mercy and Judgment, Dr. Farrar states (p. 378 ) , "Since aion meant 'age,' aionios means, properly, 'belonging to an age,' or 'age-long,' and anyone who asserts that it must mean 'endless' defends a position which even Augustine practically abandoned twelve centuries ago. Even if aion always meant 'eternity,' which is not the case in classic or Hellenistic Greek-aionios could still mean only 'belonging to eternity' and not 'lasting through it.'"
Farrar 'is probably best labeled a hopeful universalist', according to a site which explained his Universalist leanings. I note as usual the lack of evidence supplied for the conclusion.
Lange's Commentary American Edition (vol. V, p. 48 ) , on Ecclesiastes chapter 1 verse 4, in commenting upon the statement "The earth abideth forever" says, "The preacher, in contending with the universalist, or restorationist, would commit an error, and, it may be, suffer a failure in his argument, should he lay the whole stress of it on the etymological or historical significance of the words, aion, aionios, and attempt to prove that, of themselves, they necessarily carry the meaning of endless duration."
The lexical authorities (citing the relevant historical and textual data), do not support these conclusions. I see no evidence from Lange to support them either.