What am I missing? Why would you have to change your tires?
The set up you have now show your tires can carry 2535lbs per tire, a combined 5070lbs per axle. You are not carrying the 6900 pound trailer on your truck...only the hitch weight (tongue weight).
You didn't post a picture of your truck's two labels from the driver's door, but I'm guessing your axle is like most 1500s with a GAWR REAR of about 4100lbs (which with your 2 combined tires of 5070lbs is more than adequate).
The GAWR REAR can be your limiting weight.
It will most likely be your payload which will also be on the driver's door labels.