One of the chief benefits of an AR platform rifle is the weight. Compare the 6lb ARs to an 8lb Tavor or a 9lb AK47 style rifle. So, the question here is: how do you get a 6lb AR15 without sacrificing durability?
First, I want to briefly explain weight in an AR. Mil Spec ARs or actual M4 carbines use aluminum receivers. They could be made from steel, but that's not Mil Spec - steel would be stronger, but it's not Military Specifications. Aluminum is durable, but not like steel - it's more than up to the task, but the military sacrificed that extra durability for weight savings and corrosion resistance. This is just one point where the standard platform has been made to be lightweight, by design. So, I'm looking for ways to reduce the weight from the Mil Specs, without reducing durability or reliability.
The Barrel - The easiest way to reduce weight is the barrel. Now there are negative things that come from making them too light, so the question is: how light is too light? For me, from my experience and for a 16" barrel, a 22oz CHF barrel with a .625 gas block seat is the lightest I will go. I prefer a .750 gas block seat for properly pinning or dimpling, which translates to about 2 ounces, so roughly 24oz is what I prefer for my light weight builds. This beats standard government profile barrels by 8oz. Does this reduce durability? No, not at all. For anyone that has never taken off the handguards on a Mil Spec rifle, the barrel section under the handguard is noticeably thinner than the end of the barrel. This is the opposite of how high accuracy barrels for competition are designed - it should be thicker near the receiver and thinner at the end of the barrel. The extra weight at the front is essentially wasted, so shaving the contour down so it's the same on both sides of the gas block saves a lot of useless weight.
Handguards - the standard handguards are pretty lightweight, but people end up going for heavier hanguards to mount lights, vertical grips etc. However, you can get extremely lightweight, but durable, parts. For instance, BCM's KMR handguards are extremely light. A 13" KMR handguard is 5.5oz! (IF you can find it in stock.) Also, Magpul's SL hanguards are sturdy, lightweight options for people looking to add a light or vertical grip to their gun with an A2 front sight post. Look for something under 7oz, preferably under 6.
Stocks - For maximum weight savings, the best stock is Mission First Tactical's Minimalist stock. Great stock - comfortable and strong. The best strength to weight option is the BCM Gunfighter stock. It has a little bigger cheek weld and it is super strong. It offers much less weight savings than the Minimalist, but it's one of the most durable stocks out there. I would generally stay away from Magpul stocks, though they are comfortable and reliable, because they weigh too much and the new SL series are even heavier than the MOE.
Weight savings can also come from not adding the wrong things to your gun. For instance, optics can be a big source of weight. You can get a big, 10 oz red dot or you can get a 3.7 oz Aimpoint Micro T-2. You can get a 30+ oz Nightforce or US Optics scope or you can get a 14 oz Vortex. Look at the weight of your optics. Many guys add bipods, but those are relatively heavy and you really don't need a bipod on an AR15, especially not for one with a 16" or shorter barrel or a red dot sight. Some guys use the battery storage in the pistol grip or they'll put a laser on their rifle. Both of these are pointless, especially the laser - just get a red dot. Lasers (standard ones, as opposed to infrared) give up your position and are useless for distance shooting. If you're using an Aimpoint, it'll last for 5 years of continuous use on the same battery, so why bother with the backup battery? Be careful not to add things that you don't need on your rifle - that can be the best weight savings of all.
So, how do you get a 6lb AR? Choose light weight handguards, stocks, and barrels. Watch the weight of everything you attach to the gun. And, finally, don't add things you don't need.