I've got a 2016 Silverado Z71 1500, and with the stock wheels, no shake. I changed to a set of XD Monster II with Toyo AT tires and had an intermittent, sometimes horrible shake...Sometimes would rattle change in the armrest. Balance, rebalance over and over again, finally changed the tires to a Geolander AT, still no improvement. Put the stock wheels back on, smooth as glass. Roadforce balanced the XDs, swapped out two wheels put them on and it was worse. Changed from the XD wheel to a Fuel wheel with the geolanders and it is smooth MOST of the time...very rarely will I get a vibration now, and when I do, it's slight and doesn't last long.
Moral of the story is it's the wheel weight causing this problem. The truck frames are to blame for flexing, and when you change the spinning weight on each corner that causes the vibration...no amount of balancing will fix it. I had the XDs balanced 8 times in 300 miles.
The standard stock wheel/tire combo weighs about 36#...any wheel/tire combo above that can cause the unexplained vibration that will drive you nuts!