There's nothing to stop Believe Me If being played as the air to the song itself - the words were written by Moore before the story takes place, and it was quite popular. Tess and her contemporaries would almost certainly have heard it. Moore's Melodies were the Top 40 of the day.

There's something rather poignant about its meaning, of looking at one's youthful love fondly in old age - because the one thing Tess will never be is old. Death will ensure that she remains forever young and beautiful, because she is only a memory. It's an irony that I think Hardy would have appreciated.