+_1 on a tarp + tent.
Basically the lightest tent you can find plus....
A zpacks 8x10 tarp weighs 5.2 oz.
Nice thing about a tarp is you can set up the tarp
and then take your leisurely time setting up your tent, doesnt matter if it has an integral fly, change your cloths under it etc. Also allows for more ventilation in rain which is a huge advantage especially in the summer.
If no tarp the a tent with a large vestibule and a lot of ventilation.
Besides wet gear entry and setting up wet, getting stuck in a tent in the rain for a few hours or a day is no big deal but when it turns into days with the wrong tent setup is when it turns into misery. Been there done it, and even then with a decent vestibule sometimes it was not enough.
The first time I had a real taste of a week in the rain in a tent was in the 70's and that was when I started carrying a large sponge.
The biggest issue IMO is coming into a tent wet. Even before you get out to do anything, you have to make sure everything is setup right so it wont get wet coming in.
You need a place to take your boots/shoes, socks, raingear, cloths, your hat, pack if you have one. Even just going out to take a dump can be a big deal.
Although not ultralight a sweet setup would be like a tarptent squall 2, A 8x10 cuben tarp and a nano hammock for an off the ground chair/lounge.
That would weigh 2.8# plus stakes and cord etc.
Well it might be too comfy so maybe skip the hammock. Besides 2 people would fight over one hammock.