In reply to elliot.baker:
You can (and people do) abseil on paracord (3mm thick?) if you're careful enough. But as MichaHY points out - if the cord scrapes the rock too much (and bear in mind it will probably stretch more since it is thinner), it's curtains for you.
A related thing is to use thin cord as a tag line to do a full-length abseil on a single rope. E.g. if you have a 60m single rope, and want to do full 60m abseils without hauling an extra rope, you can bring 60m of accessory cord to pull down the 60m rope (requires some extra knotting at the top). I've tried it once and it worked but because of the stretch in the tag line (I used paracord) it was very hard work, and you'd be all but unable to pull the main rope through even the smallest of jams (i.e. if it got stuck in a plant) because all your pulling strength goes into stretching the tag line.