While we're at the "very old stuff" thing - there was the discovery of c 12,000 year old stones with holes in them that are suspected to be spindle whorls.
The authors and their associates did some tests with replicas of the bored stones, and it was indeed deemed possible to use them for spinning, though the spinner working with them had issues spinning wool and only was content with the results spinning flax. That was, as far as I could tell from the paper, processed the modern way with retting - and whether that technique would already have been used 12,000 years ago is another question. Most of the stones weigh between 2 and 15 g, which is also quite lightweight - though that would be depending on the technique used and the spinner's preference as well as just plain physics.
In my opinion, there is no good evidence for spinning this early; the very early threads we have were spliced, not spun. I could well imagine the bored stones to be used in some context with textile production (such as twisting two spliced lenghts of fibre together, for instance), but not really for spinning.
The article itself, if you would like to read it, can be found here. And I'd be happy to hear what you think about the stones!