Cindy,
Some numbers are in order.
2016 Tundra CrewMax, I'm assuming 4x4 weighs either (in pounds)
5570, 5645, 5670, 5690 depending.
The GVWR, Gross Vehicle Weight Rating is: 7000 to 7200 pounds.
That leaves the payload capacity at 1430 to 1555 pounds.
I see no heavy duty factory option as to drive train, suspension, brakes, or tires.
You have these options:
1. Get a larger, higher GVWR truck. or,
2. Get the smallest, lightest pop-up camper you can find and still be overloaded. The Lance 650 on a Tundra would be living on the edge alright.
I wish it weren't so. I like the Tundra platform, but it's made to look good, with good power and have a cushy empty ride.
Thousands of potential TC buyers have faced your predicament before you. Some even understood the paradigm shift.
jefe
'01.5 Dodge 2500 4x4, CTD, Qcab, SB, NV5600, 241HD, 4.10's, Dana 70/TruTrac; Dana 80/ TruTrac, Spintec hub conversion, H.D. susp, 315/75R16's on 7.5" and 10" wide steel wheels, Vulcan big line, Warn M15K winch '98 Lance Lite 165s, 8' 6" X-cab, 200w Solar