Thanks for all the suggestions.. I was away for a few days. Yesterday I noticed the same ol' problem while completing a leather backpack. Roll of "U-bond" B-69 nylon thread, which pulls unevenly from the spool (as if it were wound while still hot in the factory, or something..) This plays havoc with my thread tension which I want to set and forget. On a top-stitch it looks fine until it becomes very tight-looking (pulling up the bobbin-stitch too much), and then it goes back to "ok." Used to loosen the tension when it was too tight, but then when the spool normalized itself- the tension would become too loose. I have car upholstery which I made last week and I can see a very loose inside stitch right from where I sit, while driving. It drives me insane.
I'll try to find the brand mentioned in one of the suggestions here.. "Superior?"... however, as to my thread being 'old' I am not sure it is old.. I get these rolls from a large, busy supply house in downtown LA, (perhaps they have a lot of old stock?), and I learned years ago to NEVER buy thread in bins outside, because they are usually rotting.
I will look into the "net" suggested above, but I am not sure I have seen one before. I did try to ask the proprietors of the thread supply about this problem by bringing half a roll back to them and showing that it didn't pull off the spool very easily, but they gave me that "I don't know what you are talking about" look.
BTW I haven't ever had this problem with heavy cotton threads, but I used to prefer nylon because it is "unbreakable", and I sew through a lot of leather and canvas, and padding (I make old-car-themed backpacks)