Weight is important when backpacking. The less weight you have to carry, the more energy you have to enjoy the wilderness around you! That is why most backpackers focus on buying the lightest tent possible. But lightest isn't always best. When purchasing a lightweight tent you want to ensure that you are not sacrificing quality for weight or price.
A good lightweight tent should have:
- Good ventilation to avoid condensation build up. Although keeping the rain out is important, it should not compromise your tents ventilation.
- Wind stability. This is particularly important in four season tents that are meant for extreme weather conditions such as blizzards.
- Durability. Tents can be expensive! You want to make sure that they'll last. Make sure they are constructed of high quality material and purchase a tent repair kit to bring along just in case you need to perform an emergency repair.
- A waterproof rain fly. Should ACTUALLY be waterproof. It's a good idea to buy a tent that can create a bit of a porch with the rain fly to keep your muddy boots and other belongings out of the rain.
Here are my favorite lightweight tents.
Sierra Designs Vapor Light 2: This little tent weighs in at a mere 3lbs and 4oz. It has ample head room, a hard find in many lightweight tents, although the floor narrows at the foot, so prepare to be cozy with 2 people. The set up is quick and easy. It has a small front vestibule that will fit one large or two small packs. Another bonus to this tent is durability, according to a tester "It held up well in 20-mph winds and even a couple of inches of snow in Alaska". 
Big Agnes Fly Creek UL2: If weight is your problem, this tent is your solution. Weighing only 2lbs and 2oz (lighter than some one person tents!) the Big Agnes Fly Creek UL2 is the perfect tent for those looking to drop some weight off their pack, without sacrificing comfort then this is for you. It also comes with mesh pockets and available gear loft so it's great for longer trips, or those who just like to organize their things. A good lightweight three season tent, but the walls don't hold up that well to high winds, so keep it out of the tundra.
Terra Nova Solar Photon 2: Another amazingly light 2 person tent. The Terra Nova Solar Photon 2 weighs only 2lbs 1oz. This is a more compact tent as well, so if you're trying to save space in your bag this is a great choice. This tent has excellent water and wind resistance and a strong floor. The only downside is due to it's compact size it will be a tight fit for two adults.
Picking a good lightweight tent is an important factor in making your trips into the wilderness comfortable and enjoyable. The tents I've listed are ones that work great for me and my backpacking needs, but your needs may be different. So by all means check out the ones above, but in the end you must choose the right tent for YOU.