Given that the etymologist, Michael Quinion, in the link above admits that "your guess is as good as his" as regards the origin of the saying, here's my favourite idea on the matter.
I've always half-believed it was a play on words, in which 'full' was supposedly mistaken for 'fool'. The one thing you can state categorically about a real big girl's blouse is that it is 'full'...of big girl, that is! As a result, I imagined that calling someone a big girl's blouse was roughly equivalent to calling him a 'fool'. I appreciate that it refers to the soppy, wimpish, effeminate elements, but any man showing such tendencies could easily be considered and, therefore, called a fool as well. "You can't drink Coke in the pub, you fool!"
Right...I've taken Mr Quinion's advice and had a guess...why don't you do the same?