I just have a problem with the logic, "I was (a couple hundred pounds) overweight, that is why my tires popped."
Tires like anything else have a safety factor built in. You can rest assured that if a tire is rated for 3000lbs, it will not pop at 3001. They can't realistically expect every pickup truck owner to have constant access to a scale to ensure that they don't overload their tires.
The ratings are also STATIC, with the truck sitting on the scale. Acceleration, braking, and maneuvering put forces way in excess of the static weight on the tires, and they're not supposed to pop. A couple hundred pounds of extra static load on each tire should be nothing.
That said, it's one thing not knowing, but something entirely different if you know about the situation and don't correct it.