The aux seat is in a compartment limited to 80 lbs (the section aft of the seat is allowed 40 lbs more for a total of 120. Add the weight of the seat, your children and you are nearing the max allowed weight of the compartment. Add your weights and the fuel together and you are nearing the useful load of the airplane. That doesn't allow for the extra quart or two of oil, nor for your charts, the handheld GPS or anything else. Add a hot day to it and you are set up for disaster.
The numbers don't always equate to the reality of the situation.
Charles
