I am surprised no one has recommended a bivy. I bought a used Big Agnes 3 wire bivy this last summer and have used it a lot this year. I absolutely love it! It is light, it is comfortable and it is weather proof. I took it fishing in the rain last month and woke up floating in a large puddle/small lake on my air mattress. I was completely dry until I got out.

With a small backpacking tarp this is a complete shelter. Be aware, a tent will add 5 degrees to your bag, this will add 15. Here are some factory seconds from Big Agnes:

https://www.bigagnes.com/Products/Detail/Tent/ThreeWireBivySack

I found mine on Craigslist, but I have seen them on backpacking light as well.

J.A.F.O.