You can get double walled protection from rain, bugs and condensation for as little as 2 lbs, but currently you have to need to carry about 3.5 lbs if you want a commercially available 2 person double wall tent without significant compromises. The common compromises you'll see with tents under 3.5 lbs are small dimensions, non-freestanding designs anbd silnylon floors. In my opinion, 30D silnylon floors (1200mm waterproof rating) are not signficantly durable or waterproof to be used without a groundsheet, so you need to consider the weight of one of those when comparing it to other shelters with more durable floors. Silnylon floors are also super slippery (ie. you'll slide around the tent if the ground isn't level) which can be remedied with silicone sealant, but that adds weight and make the floor a dust magnet.
The lightest double walled shelters are the trekking pole supported tarp + inner net tent offerings from SMD (Haven) and MLD (DuoMid). The DuoMid combo is lighter because you can get a cuben tarp (a cuben version of the Haven tarp is rumored to be in the works). I would personally choose the Haven though because it uses two trekking poles so you get more headroom and avoid having a pole inside your shelter. The DuoMid is also very small inside for two people. While the Haven offers a more reasonable amount of room, the headspace is limited because it uses two trekking poles so the headroom is only high between the poles. You can't sit up everywhere inside the shelter like you may be used to with a traditional tent. These shelters also have the disadvantage of not being freestanding, which isn't a huge deal unless you camp a lot on sand, snow or flat rock.
The next lightest option is the Big Anges Fly Creek UL2 at ~2.4 lbs. It's a double wall tent that uses poles. The major compromise here is interior volume and a silnylon floor. The sidewalls slope inwards heavily so it's not big enough inside for two people to sit up in at the same time. I personally would only use it with two people if we were just sleeping in it. It wouldn't be comfortable to wait out a rainstorm in.
Next lightest would be the Big Sky International Evolution/Revelation tents at ~2.7lbs. These are tempting tents that are adequately roomy. The main compromise here is the use of 30D silnylon for everything including the floor.
Next lightest is the MSR Carbon Reflex 2 at 3 lbs. Unlike all previously mentioned tents, the CR2 has a more durable and 10,000mm rated floor. It also had the most headroom of the tents mentioned so far. I would say this tent has enough interior room to be livable for two for more than just sleeping. The floor area isn't huge but it's adequate and the interior volume is good because the side walls are vertical so you get lots of headroom. The compromises you make with the CR2 are the single door, small-ish floor area and that it's not freestanding which can be a pain on sand, snow or rock if you're not prepared. It's also not the biggest tent inside, but it's acceptable if you understand what you are getting. My wife was happy sharing the CR2 with me...other guys maybe not so much. Make sure you have proper stakes if you set it up on sand since it's not freestanding. Price is high at $499 but you can find them on eBay for ~$100 less.
Next is the Big Anges Seedhouse SL2 also at 3 lbs. It's got a silnylon floor and borderline headroom, but it is freestanding and it has a decent floor size.
Next lightest is the Tarptent Scarp 2 at about 3.4 lbs. The Scarp 2 had a large floor area. Like the Big Sky International tents, this tent uses a silnylon floor so you have the same waterproofing, durability and slipperyness questions. The good things about this tent is the optional 4 season mode, optional fabric inner tent and large floor area.
Heavier than this you get a bunch of mainstream tents that have pretty much no significant compromises in exchange for the 3.5-4 lbs weight. There is a lot of tents in this category. Off the top of my head there is the MSR Hubba Hubba HP, Mountain Hardware Skyledge 2.1, REI Quarterdome T2, Big Agnes Copper Spur UL2, Sierra Designs Lightning XT etc. From this list, some standouts include the REI tent for it's value (they go for $150-$175 on eBay) and the Hubba Hubba HP for it's fabric inner which makes it well suited to light 4 season use and for dusty or sandy conditions where blowing sediment is a concern.
Many of the tents listed can potentially be lightened though the use of lighter poles (ie. Fibraplex carbon poles) which can save up to 1/2 lbs in exchange for a lot of cash ($100-$175). You can also shave a ton of weight by replacing the fly with a MYOG cuben fly. I'm currently working on a MYOG 0.75oz Cuben fly for my REI Quarterdome T2. The original fly weighs 23oz and I think I can make a cuben one for 8-10oz. This will put me at about 2.8 lbs for a roomy freestanding two person tent with a highly waterproof and durable floor. I've also ordered Fibraplex carbon poles which should weigh 8oz instead of 16oz so I'll be down to about ~2.3lbs for a freestanding, spacious, dual entry, adequately durable and waterproof shelter.