Kurt Weinreich of Olympia sponsored a series of initiatives a few years ago, and apparently had some interest in promoting his initiatives by shrinking the size of the initiative petition to "post card size." His thought was that he would mail out post cards to a list of supporters and they would mail them back to him. Neither his idea or Weinreich's petitions have been seen in the last few years, but he did give some interesting HB 1014 back in 2003.
Apparently there are no documents on why the original 1906 size of 12×14 size (even according to the SOS office). What eventually happened was that since no one made 12×14 sized paper, printers had to cut down larger pieces to get to that size. I assume 12×14 had something to do with a standard size of newsprint that eventually changed.
In the early 80s the size was changed to the current 11×14, but even now that isn't a standard size anymore. I assume in the 80s it was, because why else would they have changed it to that size? Most initiatives now, or at least the ones I've looked into, print their petitions on 11×17 sized paper, which is the standard Tabloid size.