What is the meaning of “well-a-well”?

Solution 1:

The OED attributes this now rare construct to Scottish and Irish English (northern) with the sense of 'expressing surprise, anticipation, resignation, or acquiescence'. It gives among several examples:

The old woman tried to comfort her, beginning with her accustomed, ‘Well-a-well!’ (Elizabeth Gaskell, Mary Barton, 1848) and Tam simply wad say, ‘Weel-a-weel, I'll jist by your counsel be guided.’ (David Willox, Poems, 1898).