1. to damp, to tone down, to attenuate (Not very common, as there are plenty of other options. NOT used for physical weakness. )
Opposite (closest): verstärken
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.