1
general::
After a while, soon, as in She'll be along by and by. The expression probably relies on the meaning of by as a succession of quantities (as in "two by two"). This adverbial phrase came to be used as a noun, denoting either procrastination or the future. William Camden so used it for the former (Remains, 1605): "Two anons and a by and by is an hour and a half." And W.S. Gilbert used it in the latter sense when Lady Jane sings plaintively that little will be left of her ‘‘in the coming by and by," that is, as she grows old. (Patience, 1881). [Early 1500s]
American Heritage Idioms
2
general::
Phrase(s): by and by
at some time in the future; as time passes. • The weather’s sure to clear up by and by. • You may think your heart is broken, but you’ll feel better by and by.
McGrawhill's American Idioms And Phrasal Verbs