Well I guess I'll cast the disenting vote here. (this is based on my understanding of the regs & driving a rig. Your experiences may vary)
The weight rating of the trailer is based on the axle ratings not the opposite. In other words, the 7K rating is a number generated by the axle load capacity not a set in stone number for the overall trailer.
I have never been asked to separate the trailer from the truck or even seen a calulation done with that respect. I've rolled thru weigh stations, both POE and portable and this is the way it's gone every time.
the front tractor axles first, then the rear tractor tandems, and then the trailer tandems. (if portables are used then each axle at a time).
They look for overweight axles (or axle sets) and overall weight. If I'm over the axle rating; I'm busted, or if I'm over my registered weight; I'm busted.
If say your weight is distributed so that each trailer axle weighs 3400 lbs, but the rear truck axle is over then you'll probably get cited. (but on a good day they just might let you redistribute your weight to try and bring it down.)
If your under on all your weights, you're good to go.
Some years ago, a buddy of mine rolled thru a POE scale 6K over max (80K) and was able to convince them that it was due to ice buildup on the pipe he was hauling. They bought it and gave him a hour to bust the ice loose and re-weigh.