The link above to a previous thread here has a link to a supplier that has amsteel 7/64 (2.7mm) for .14 a foot. It is rated at 1200 lbs and weighs .3 lbs for 100 ft. I purchased mine from apsltd but this price is better before shipping.
I use the amsteel on everything but the rings then I use the spyderwire which is really basically the same thing with a cover. I used wbg's way of using a sheetbend to the treehugger and spyderwire down to the rings with a garda hitch. This is much lighter than the webbing.