I have a 2011 GM truck with the new fully boxed frame and so the rear anti-sway bar was not needed. In the front the stock anti-sway bar is 1.25 inches thick so as good as any aftermarket product.
I added Supersprings to help carry the load of a heavy camper on my 2500HD truck. Same approach as GM takes to increase load capacity to create a 3500HD truck on the assembly line. No sagging at the rear of the bed with the camper fully loaded for a trip.
I did improve the handling by upgrading the factory tires from ones rated at 3195@80 PSI to ones rated at 3750@80 PSI. Less sidewall flex with the camper load and this improvement was primarily aimed at increasing the load capacity by 1100 lbs. as the tires are the weakest link.
If the bed sags down at the rear with the camper in the bed then add Supersprings or air bags or additional leaf springs to the existing leaf pack.
For sway check your tires and verify they can handle the total load of truck and camper and gear by having it all weighed at a CAT scale for $10. If you need new tires then do this before adding an anti-sway bar.
Some trucks like the Ford trucks in particular have a frame that flexs a good deal more with a load and adding a heavy duty anti-roll bar at the rear is necessary for hauling a heavy camper around. 2011 and later GM/Chevy trucks and 2013 and later Ram trucks should be fine without adding a new rear anti-roll bar.