A quick look at the meaning of "schweben", where it comes from and what it has to do with imagination and blabbering.
schweben, vorschweben, der Schweif, abschweifen, ohne Umschweife
The core idea of this root was:
bending, swaying, swinging
It’s still quite visible in German words like schwanken and schwenken and even in Schwanz (tail). Just think of a dog waving it :).
The adjective schwach started out as bendable, from where it is not far to its current meaning weak.
The English etymological sources I am using do not mention this root.
But according to the German sources, it would be the origin of the English words to swing, to sway and possibly also swag.