The purpose of the airbags has less to do with sway and stability and more to do with steering. When you exceed the load capacity of these trucks, there is so much weight on the rear wheels that the front begins to "float". What happens is that you get an oversteer situation and the truck tracks poorly. If my airbags are not inflated properly, I can't keep the truck in a traffic lane at 55 mph. By pumping up the airbags, you raise the rear end higher than the unloaded position and this distributes more weight to the front axle and restores control.
Based on a couple of years of reading this board, it seems that airbags don't seem to be necessary on the 1-tons. But if you have over 2000 lb loaded on a 3/4 ton truck, you probably want airbags. The downside of airbags: You have to keep 10-15 lb of air in them when empty and this causes the rear end of an unloaded truck to hop a bit more than stock.