The Gatewood Cape by Six Moons Design is probably your best bet.
It is designed to be a ground shelter, but it could be used over a hammock too.
When used as a ground shelter, it offers full 4-side coverage, and can be pitched down tight, or also several inches off the ground for ventilation. It's very hard to beat if you want all 4 sides covered, with a door that you can open and close.
It has been around a while, and has a reputation of being able to stand up to some storms and wind if it's pitched well.
There is an optional "Serenity Tent" bug-tent with floor that can go inside, making a double-walled tent. Fights both bugs and condensation woes. It's separate, so you don't have to bring it or use it on days when you think it wouldn't be wanted.
Together, they make quite a lightweight double-walled enclosure, and in fact it would be one of the lightest double-walled shelters anywhere, at about 19 ounces.
Not the world's lightest shelter for sure, but for a double-wall it's very light. And it gives dual use as a poncho.
Speaking of the poncho use, some like it and some don't think it's the greatest for a poncho. It's long, and it has arm slits. Some don't like the arm slits, and some say it drags too low and doesn't have a good tie-up belt. But, it's a poncho and it covers you and your pack, and it has a hood, and it's silnylon and weighs 11 ounces by itself. It's certainly better than no poncho, and it will do the job.
Considering the dual-use nature, it might be the overall lightest and most versatile piece of gear around, if you can work it into your way of doing things.
Probably not for everybody, but for some people it is probably the best combination product around.
Mountain Laurel Designs also has a poncho-tarp for just a little higher price, and it's probably better as a poncho, but probably not as good for coverage and protection as a shelter, and it is a little smaller.
I guess it depends on which functions are most important to work the best, and what you can compromise on.
Alternatively, if you are rich, you could buy all separate items made from cuben fiber and still come out lighter, but it might be more bulky to carry it all.
Maybe a cuben Gatewood Cape might be nice, but they don't make one(as far as I know).
I think it comes down to whether you want to carry a poncho for your rain gear. If you do, then these poncho-tarps offer something good. If you'd rather use a raincoat, then these poncho tarps lose their dual-use nature, and then they just become shelters which are not as light weight as you could get from some other plain shelter tarps.
One other option is to just get a flat tarp out of whatever material you like best, in the size you want, and wrap the tarp around you like a cape in the rain, with part of it over your head like a hood. That can be done too.
But, to meet that "enclosed tent" part of the requirements that you stated, the Gatewood Cape is your best bet. Everything else is a poncho-tarp, and the Gatewood Cape is a poncho that actually makes a floorless tent when you set it up. It's essentially identical to the SMD Wild Oasis tent, but it has a hood. And it can be paired with the matching bug-tent made to fit it, which gives bug protection and dual-wall condensation protection.
It's a pretty nice package, and SMD is fairly well-known and respected.
