Unless you pile bricks over the axles, you won't put that much weight on them, even if you load the trailer to the max. Don't forget, much of the added weight of your "stuff" is forward of the axles, in the basement, front compartment, and bedroom. Our 3670 also has 7000 lb. axles and a GVWR of 16000 lbs. Loaded for travel (empty tanks), the weight on the axles was 5650 lbs. front and 5925 lbs. rear according to the scales at the Goshen rally. Total towing weight of the trailer was 14525 lbs. 2950 lbs. of that was on the pin.
The slight imbalance in my axle loads is probably due to the trailer riding a tad nose high after installing the 5th Airborne pinbox, thus putting more weight on the rear axle. I'll experiment with dropping the hitch head a level to see if it helps. I do have to watch the clearance over the truck bed rails, though. No problem on the roads, but when backing into an uneven/rough grass/dirt site, it might be a factor.