Absolutely the lightest would be cuben fiber (see ZPacks), but it's definitely not for those of us of modest means! I'd suggest sewing your own out of a high quality silnylon--It will hold up well for years (unlike plastic or other el cheapo substitutes) for years, but won't break the bank.
Size: The problem with a smaller size tarp is rain blowing in under it, requiring a bivy to protect your sleeping bag, which adds to to both price and weight. In other words, you might as well start with a tarp that's large enough that you can lower the sides-to the ground if necessary-in really nasty weather and don't need a bivy.
May your trails be crooked, winding, lonesome, dangerous, leading to the most amazing view--E. Abbey