"The Weaver and the Factory Maid always make me think of Lancashire because my grandfather worked in the cotton mills there."

From what I remember of an interesting article by Roy Palmer in the Folksong Journal, Bert Lloyd stitched together the version that we all know from several different sources, including one which included the line: "The finest lass in Morley town, she walks around in a fine silk gown". So not only was she from the West Riding, she was posh as well.

"The White Hare of Howden is a traditional Irish folk song, but it always reminds me of Yorkshire because Howden is in Yorkshire."

Irish?? I always thought it was collected from Joseph Taylor in Saxby, Lincs., not too far away from Howden on the other side of the Humber. Harry Boardman, however, (see Mark's link) claimed it for Lancashire and sang "Oldham" instead of Howden. And I believe another version was collected quite recently in Devon by a Mr. Lakeman.