The lightest, cheapest tarp you can get is plastic, 6mm - 10mm, using pebble wrap tie off points. Won't last long but you can get a trip or two out of it if you're careful, and it's waterproof.
an 8x10 silnylon tarp from OES (cottage gear industry, may have a wait time) http://www.outdoorequipmentsupplier.com/rectangular_tarps.php
Many options for poncho shelters, here is one of the more affordable: http://www.jacksrbetter.com/Poncho-Shelter.htm
You can do it cheaper... by getting factory seconds of silnylon from OWFINC or Seattle Fabrics, $6-7/yard if they have any, and sewing it yourself. Silnylon isn't just nylon. It's treated with silicon. It's about the cheapest option you can get without going heavier. You can go lighter but it will cost you more, unless you're ready to settle for the cheap flimsy plastic approach.