Michael Quinion, in the link in the answer above, says about the origin of this phrase that "your guess is as good as mine". In other words, nobody really knows, so here's my guess. It is possibly just 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 a man a big girl's blouse might be roughly equivalent to calling him a 'fool'. I appreciate that it refers to the soppy, effeminate, wimpish element, but any man showing such a tendency could easily be considered and, therefore, called a fool as well...as in "You can't drink Coke in a pub, you fool!"
As a matter of interest, Quinion also refers to "Well, I'll go to the foot of our stairs!" I'm convinced that that was originally simply a euphemism for the much cruder "Well, I'll go to f*&^!" Note the fact that the f sound is maintained and, having said the word foot, clearly something had to be added to indicate what it was the foot of.