I agree that you don't need super strong lines, but I'd be tempted to go with something stronger than 20 lb test. I have 60 lb spectra fishing line that is .016" diameter and 200 lb that is .030" diameter. (You can get Power pro cheap off Ebay.)
I'm willing to bet you could "sew" both right through a sleeping bag with the right size needle. Weight??? really low... Strength???? pretty good.