'Dubya' is a mocking term for George W. Bush. It comes from his heavy texan accent (well, maybe not that heavy), and his insistance of using the middle 'W' in his name. The result of which is your hear "George Dubya Bush" quite a lot, even from people without said accent.
I think it was columnist Molly Ivins who popluarized this moniker, as well as saying that to pronounce it correctly, you need to make it one syllable. Obviously, not everyone can do this.
Although I would certainly try not to use "dubya" in everyday/public speech, I am quite fond of "y'all".
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