I was looking for the words to the song, have a few British folk song books, and a couple of Geordie ones an' all, but no Waters of Tyne! The first link I clicked on had the link to here, and it says there:

[1979:] This exquisite lament was first published in 1793. The tune was taken down almost a century later from an old man at Hexham, Northumberland. (Palmer, Country 143)
The first link is here:
http://www.mysongbook.de/msb/songs/w/watersof.html

By the way, I'd go with the Scandinavian origin for hinny, despite what it says in the dictionary. It's not only the North that has Scandinavian words which beat out the Anglo-Saxon ones, even EGGS is from the Norse, as is, I believe, window, from "wind's eye."
Not to get pedantic however, where does the endearment 'pet' come from. ;-)