It's probably the tread itself. A heavy duty traction can get squirmy sooner than an AT which is sooner than an HT.
Even if the new tires were a D rated tire, that should not effect hanging, if the tire was rated for the load. I've referred towing with an 8ply D rated 265-75-16 vs a 10 ply E rated 245-75 or 235-85 16" tire. All three sizes have a max carry load of 3000 lbs.
Another potential issue, is the tire wider than previous, if so, your rim may be to narrow, or on the narrowest it can go on, this will will cause squirm too, in heavier load or trailer tow conditions.
Marty
