The Equinox siliconized tarp that I have is very light (the 10' x 12' size weighs less than 19 oz) although it is a bit pricey at $85.00 US. These are available from Campmor out of Mahwah, NJ. Also be aware the newer style tarps are a dark green, not the older bright green version shown on the website.
I have an 8 by 10 Equinox and I think it is about 12 ounces. I'm planning to use it as a primary shelter for a backpack trip this summer.
I found this video on setting up a tarp and I emailed this guy and asked why he "hung" the tarp from the ridgeline rather than just throwing the tarp over the line. His response was that he was taught to do it this way. He asked me to try it both ways and see which I prefered and let him know. Very nice guy and very helpful.
I'm afraid that too much stress on the tarp (from wind and/or precipitation) would tear the ties off of it. Seems like running the tarp over the ridgeline would provide much more support than "hanging" the tarp, and I think securing the tarp to the ridgeline with the prusik hitch would eliminate the drips coming under the tarp (running down the ridgeline and dripping at the low point).
http://www.youtube.com/watch?v=bjMmla9DSzo&eurl=http://www.bushcraftnorthwest.com/articles/articles.htm