yes, you may.

just kidding,  my current rig is a 2002 chevy trailblazer with a BP 2h slant w/dress that comes in at 6000# with horses and tack. i use an "equal-i-zer"  WDH and a prodigy brake controller. it does not sway, is not pushed off the road by 18 wheelers, stops with no fuss, and i suspect it will accelerate beside any FULLY loaded diesel dually.  that being said, i will have a larger truck in the near future, was going to be sooner but this pitiful little beast did so much better than i thought it would, the plans got pushed off.  there are certainly better tow vehicle choices out there, as at the very least i dont consider an automatic transmission appropriate for towing.

i would agree with the "wear" issue, but since the OP stated it would not be every weekend(myself and many others also in this same situation) that will likely not be an issue. and accelerated wear is not a saftey issue unless proper maintenance is not followed.

as for "control", i fail to see what advantage a 1 ton has over a 1/2 other than 2000# pounds? take loaded 3h trailer,say 8000# and a 1/2 ton 5000#....13000# total. so with the 1 ton we have 15000# total. heavy wind in the open sucks, period, ive driven through the west side of the country for about a year and even 80000# of tractor/trailer is not immune.

JUST SPECULATION.......now ive never blown 2 tires at once, but i doubt i would even concern myself with how heavy my truck was at that point.  just have to rely on the training.....do NOT stomp the brake, look where you want the vehicle to go, slowly release the throttle, slowly apply the brake so as not to disturb the vehicle supsension/vehicle attitude and in theory pull to the side of road......served me well over the years. small truck, big truck, heavy load, no load.

so when handing out advice, which would you rather have in the hands of a novice(not refering to OP), 13000# out of control or 15000#??? doesnt make much difference to me. training/experience is what matters