Alas, the word "tarp" has several meanings. From the sounds of it, you're describing some kind of simple, single-layer sheet that has a bit more shape and even support than just a waterproof sheet strung between some trees. Right? If so, look to MSR's Trekker Wing, which is sort of a "shaped" tarp that uses two poles for support and then ties out to stakes or trees. It weighs less than two pounds and costs $190 (www.msrcorp.com). GoLite's Den 2 ($199; www.golite.com) weighs a touch more but offers a lot more weather protection.
For a more robust shelter, just go with a full tent, albeit a light one. Mountain Hardwear's Waypoint 2 ($250; www.mountainhardwear.com) is the ticket here, at just over three pounds and boasting good ventilation and exceedingly good weather protection. This may also work better if what you mean by cool-weather camping is outings in fall and early spring, when nights may be just a little too brisk for only a tarp and sleeping bag.
As to your bonus question, you're right: digging a rain ditch around a tent isn't very ecologically correct these days. That presents a challenge when using a top-only shelter such as a Trekker Wing. And I don't have any really good advice, aside from inspecting your proposed campsite very judiciously to ensure it's on relatively high ground. I suppose that creates a good argument for a full tent, with a floor, such as the Waypoint. I've been poured on in that thing, and stayed dry even as little rivers flowed around the tent.
Anyway, hope that helps. Happy hiking this summer!