On my last rig with a GVWR of about 10K, I upgraded to 16" tires and wheels. It was a big expense, and the wheel wells barely had the room for 225/75-16's.
Our current TT has a GVWR of 8849lbs, I upgraded to GY Marathons in LR D but opted to stay with the 15" wheels it came with.
That gives me more tire capacity, than the entire rig weighs including the tongue weight. FR shows your model at about 1000lbs less than mine, so I think you'd be fine just going up to LR D's and staying with the original wheels.
The 15" wheels don't have that much capacity (neither do the axles), but I'm not seeing posts about wheel failures.