Have you thought about using Onion Skin paper? It's thin, just 8 or 9 lbs weight, VS 18 to 20 lbs. weight for regular copy machine paper. Yet it's strong too, so it will go through a regular copy machine without problems, and will not tear if you're copying on it. It's what I use, and then I just pin it to the fabric, stitch away, (smaller stitches), and it tears away easily. Any problem spots and a dab of water with a Q-tip, wait a minute, and it comes right off. Love the stuff! Here's one source, although I'm sure you can find it at your local Office Max or Staples:
http://www.thepapermillstore.com/pap...-per-ream.html
Another thing I have done is copied it onto regular copy paper, and then used my rotary perforator to make a grid of perforations on the paper. Not quite as good as the onion skin, but will do in a pinch. Really helps to release the paper from the fabric to pre-perforate the paper, or sometimes just the lines, if they're not too intricate.
Warmest Regards,