Something caught my eye in an Ask Metafilter comment just now:

“I experienced it as a light trance state similar to the one I was in for smoking cessation (which, by the bye, worked amazingly well — I haven’t had a cigarette since my first hypnosis session more than 22 yeras ago).”

The version I’m accustomed to is “by the by”; I have no idea what the story behind this idiom is — an alternative to “by the way”, essentially, but from where? — and so it doesn’t seem surprising to me that different folks might analyze “BY” in different ways.  What struck me was the asymmetry — that it was neither “by the by” nor “bye the bye”, which I can only figure I thought was odd because it implies an analysis of the idiom that treats the two BYs as semantically distinct items instead of just a repition of one.

Is that actually odd at all?  I don’t know.  Idioms are funny beasts, that way; I have no idea what folk etymolgies might be deployed for “by the by” (and variants), but I’d be surprised if they didn’t vary from person to person.  And speaking of variants, some quick google counts:

by the by: 7,500,000
by the bye: 605,000
bye the bye: 21,300
bye the by: 1,930

And with “way”, for comparison:
by the way: 10,300,000
bye the way: 300,000

So “by the by” isn’t much less common than “by the way”, which surprises me a little; “by the by” feels a lot more stilted, affected, like something you’d choose to say rather than something you’d just say.  But that may just be an expression of what I grew up around in my family or my region.

And the argument toward symmetry I made earlier — that repetition of a single semantic unit would beat out two distinct but homophononous versions, “by” and “bye”?  Blown out of the water, consider how many more matches there are for “by the bye” than for “bye the bye”. 

So, new improved theory: the “by the…” variants trounce the “bye the…” variants, since the former is a pretty plausible prepositional construction where as the latter is not so much.  This effect, the preference for leading “by…” over leading “bye…”, is a lot stronger than my symmetry argument; but within either variant (”by the…” and “bye the…”), the version that features repetition has a lot more hits than the version with two distinct semantic units.