About the most any of the F350 srw can carry in the bed (over the rear axle) before exceeding a tire/wheel or rear spring pack is around 3800 lb payload in the bed (est).
The new gen crew cab 4wd long bed one ton srw trucks are heavy with rear axle weights in the 3400-3500 lb.
A 16k trailer may have around 3200-3400 lb hitch weight.....a 12K dry weight = around 2400 lbs. A 14k figure would be a good guess at a loaded weight.
Of course the truck won't have any issues pulling a 16k trailer. Your going to have a max or close to max loaded truck (rawr) which I personally don't have any issues with operating at at max ....your call.