Ayto doesn't expound where the late 14c. meaning of ‘once more, anew’ sprang from? Is "once more, anew" related to "in a direct line with, facing" or "in the opposite direction, back"?
The underlying etymological sense of again is ‘in a direct line with, facing’, hence ‘opposite’ and ‘in the opposite direction, back’ (its original meaning in Old English). It comes from a probable Germanic *gagin ‘straight’, which was the source of many compounds formed with on or in in various Germanic languages, such as Old Saxon angegin and Old Norse íg gegn. The Old English form was ongēan, which would have produced ayen in modern English; however, Norse-influenced forms with a hard g had spread over the whole country from northern areas by the 16th century. The meaning ‘once more, anew’ did not develop until the late 14th century. From Old English times until the late 16th century a prefix-less form gain was used in forming compounds. It carried a range of meanings, from ‘against’ to ‘in return’, but today survives only in gainsay.
The notion of ‘opposition’ is carried through in against, which was formed in the 12th century from again and what was originally the genitive suffix -es, as in always and nowadays. The parasitic -t first appeared in the 14th century.
Word Origins (2005 2e) by John Ayto, p 11 Right column.