Where did the word "yourn" originate?

Solution 1:

Yourn, ourn, hisn, hern, theirn all originate in the Anglo-Saxon Mid Anglian dialectal grammar (Cambs, Hunts, Beds) and contain the pronoun weak ending still present in mine and thine. My family originated in Cambs and evidently retained its dialect speech even when the Industrial Revolution obliged them to move to London in the 1830s. My grandfather said yourn, etc and my father said it (and I do!) whereas my grandmother's family and my mother's family came from different parts of Suffolk (East Anglian dialect) where they didn't say it.

They are not contractions of your one or your own at all. The Samuel Pegge quotation is correct - the ancient grammar lingered longer in Mid Anglia than elsewhere which is why it has survived. The Americans and Australians inherited it through colonization.

Solution 2:

OED says it's modelled on mine, so I believe it comes from the following analogy:

my is to mine as your is to yourn

The more common word yours comes from the following constructions:

her is to hers as your is to yours.

our is to ours as your is to yours.