I haven’t seen them, but I expect them to be similar to the records they used to give away as marketing gimmicks: so thin that they weren’t rigid under their own weight. You could roll them up.

If you decrease their diameter, weight would go down even further.

Edit: these are called Flexi Disc (https://en.wikipedia.org/wiki/Flexi_disc). you can even make records out of plastic-coated carton: https://en.wikipedia.org/wiki/Cardboard_record