5:08 p.m. on February 13, 2013 (EST)
There are a great many "tarp-tents" on the market these days.
By tarp-tent, I gather your talking about the newer hybrid single wall shelters with bug screens and floors and such - rather like tents but without the traditional rain fly and usually ( but not always ) made out of lightweight silylion?
The short answer is -They work fine.
But - It is also fair to say that they are more dependant upon proper setup and site selection than say, a traditional freestanding dome tent.
Many are made from silnylon, which isn't as waterproof as traditional tent fabrics, and tends to sag a bit when wet.
Note that not all "tarptents" are made equal, and they vary significantly in design, ruggedness, ease of use and weatherproofness.
I own two, made by the company called "Tarptent", a Squall 2 and a very similar but huge Rainshadow 2. These are fantasticlly light tents, and my wife and I don't mind single entry tents a bit, so they work well for us.
You can see 'em here, as well as a pile of other tents including lightweight double wall tents -
http://www.tarptent.com/index.html
I quite like my tarptents but I have been lucky and have yet to have them in nasty conditions.
Mine are non-freestanding designs, and like all such tents if a stake pulls out the tent comes down on you. Use the side stake outs and stake or tie 'em well, and I think these tents withstand bad weather fine - These have been used for multi thousand mile hikes, and many folk just love 'em.
But they are airy, and that may turm some folks off. To keep condensation to a minimum they are designed for max airflow, and you can't seal the tent tight even if you wanted to. If you look at the Squall 2 on the Tarptent web site you'll see the door is just mesh, covered by a big beak. Doesn't bother me, I like regular flat tarps and got started camping under those, I don't mind the open-ness, so to me the added bug screen and bathtub floor of my Tarptents is a fantastic bonus.
One Tarptent that gets rave reveiws that you might want to look at and is more like a "traditional" tent is the Double Rainbow. It is less than three pounds, about 30 sq. ft, double doors and great dual porches which makes it feel bigger and provides dry entry during the rain and a great place to cook over your stove ( WARNING! silnylon tents are very flamable! Much more so than traditional nylon tents. I'm not saying don't cook under the porch, but do be carefull ).
You can even get a clip in liner making it a true double wall tent.
It is not a trekking pole tent and has a single big arching pole, making it quite weather worthy and easy to set up. If you do use trekking poles, the tent can even be set up as a free standng tent!
It is $ 275 though, a bit over your budget but maybe you could find a used one.
Heh, can you tell I want one?