Other English speakers I know complain about our orthography: bought, caught, draught, etc. But, yet, here we are with a “word” pronounced “of” and spelled “‘ve”! Now that’s awful orthography!
In my household I'm the English nerd, although I have no degree behind it. I'd correct my wife when she wrote "would of" but then I listened closer when she talked: She wasn't saying "would've" she was saying "would of".
That's when I gave up. There are a million other reasons to love my wife, and her proper use of 'would've' wasn't one of them to begin with :)
She does not. They are the same to her. We're also native speakers from the Reno NV area, which is heavily influenced by Sacramento and San Francisco language.
others have covered the correct full form, but to the issue of the pronunciation, it's not pronounced "would of" it's MISpronounced "would of". You can make any weird confusing pronunciation you want out of anything if you're willing to say it "wrong". The correct pronunciation of the contraction, as another hinted at is basically "would have" without the h and the a becoming an sound "uh" instead of an "ah" sound.