Well, this is what the Googles gets me (with a peek at the OED):
Owt and Nowt are shibboleths for Yorkshire: they are very common dialect words. The historical pronunciation seems to be something like /ou/. They are indeed derived from aught and naught; the spelling with an au is from Early Modern Southern English, and Middle English usually spelled them as ought and nought. Brought in Yorkshire rhymes with owt. (Remember that in Middle English, the <gh> was a kh sound.)
On the other hand, the <ou> diphthong which normally rhymes with <ow> in English is either -ah-, in the West Riding (e.g. Sheffield), or -oo- in the North and East Riding: abaht, aboot.
Hence Nathan Morris’ answer to Could someone tell of “owt” or “nowt” regarding Yorkshire?
A can tell thee owt tha wants to know abart.
[I can tell thee aught thou wants to know about]
EDIT:
Joseph Boyle asks whether the aboot of East Yorkshire is related to the aboot of Canada and the US South Highlands.
The Yorkshire and Scots aboot really is pronounced aboot. It is a an archaism, representing the pronunciation of <ou> before the Great English Vowel Shift. (Middle English used the French pronunciation of <ou>.) Notice that Yorkshire keeps <ou> and <ow> separate.
The Great English Vowel Shift changed iː to əi to ai. It’s why reconstructed Shakespearean pronunciation sounds like a pirate: West Country English, on which Hollywood pirate talk is based, has kept the older əi pronunciation.
What happened to Middle English i: also happened to uː : uː > əu > au.
- uː is the original Middle English pronunciation, preserved in East Yorkshire.
- au is the usual Modern pronunciation.
- aː is a further development from au, found in West Yorkshire.
- əu is the missing link between uː and au. It is how Shakespeare would have pronounced about. It is also how Canadians and Southern Virginians pronounce about: Canadian raising – Wikipedia, [əbəut].
So Shakespeare would in fact have sounded like a Canadian pirate.
The chain of development is East Yorkshire aboot > Canadian and Southern Virginian əbəut > standard English about > West Yorkshire abaht. Logically, that tells you that the missing link pronunciation used to occur in West Yorkshire as well, and eventually gave rise to abaht via about. But there is no reason to think that there is anything Yorkshire about Canadian raising. It appears to be a general archaism, although not one that Wikipedia has much history on.
And yes, all my information is from Wikipedia.