Chaucer and other early writers called a frivolous or giddy girl a gig, and such was indeed slang usage even to the eighteenth century.
So, presumably because she seemed to fizz or sputter as she ran gadding about, such a girl or woman became a fysgygge, as it appeared in sixteenth-century spelling.
Since then varied meanings have been applied, all associated in one way or another with fizz.
