While certainly not as light as I'd like to be, my setup is on the frugal end and has all the requirements you're asking for.
I went with a Golite SL1 nest to do the duty of a bugnet/ground cloth (weight = 16oz, mine came in at 15.5 on my cheap scale without the stuff sack), and a Kelty Noah's Tarp 9 (29oz per manuf, haven't weighed mine).
I'm using UL throw line for cordage, and the whole kit cost me under 120$ buying everything on specials.
If I could do it over again, I'd just ask in the GS section for an 8x10 siltarp instead of the Noah's Tarp purchase to save on weight for the money. I'm not against used gear at all.
The extra room under the tarp is really nice when it's down pouring though.