I think this is slang that has entered the language in the past few decades - I don't recall its use in my younger years. I would go by the definitions at:
www.peevish.co.uk/slang/w.htm (feeble; emotional; effeminate)
and
www.artistwd.com/joyzine/australia/strine/w-3.php (
1. weak; feeble; spiritless. 2. stupid; senseless)
I think I've generally taken to understanding it as a contraction (and development) of "wet behind the ears" - see for example:
www.answers.com/topic/wet-behind-the-ears
maybe also associated with limpness which may result from being wet. But maybe I'm just guessing.