My 2014 Sierra shake is fixed! I've been dealing with this issue since the truck was purchased new in May 2014. I was convinced it was the OEM tires, had them balanced and rotated several times with same results. I replaced them with Michelin Defender tires and had same issue. I took it to a GM dealer, they charged me to re balance the tires and said it "meets GM standards" for ride quality. I called BS on that. The truck still had the same issue so I was going down the axle/driveshaft route to see if that would help. I took it back to the shop I purchased the tires from (Discount Tire) and asked if they would road force balance the tires. They checked for a vibration first and one tire was out of balance. This shop did not recommend road force balancing my tires since they had around 6K miles on them. The shake was not as bad but still present. After a few months figuring out what to do, either trade the truck or just deal with the poor ride. I took it to another Discount Tire shop and asked if they would road force balance, they had no problem road forcing the tires. The tech showed me where one tire had weight all over it and said this should not be. After checking all the tires one was at 38, the tech said anything under 20 is good. Once road force balanced all tires were under 20. I was super surprised when I drove it and the shake is gone! I did the glass of water test and not a ripple up to 90 MPH. I didn't go any faster than that since I was catching traffic. I feel as if I have a new truck now and really enjoying it!
My 2014 1500 has the Texas package with 20" wheels.
Bottom line try different tire shops before you give up. They all have balance machines but the tech operating it needs to understand what is going on.