You will stay hooked up. As you pull on you will see the sections of the scale. One for your front tires, one for your rear tires and one for the TT or 5er tires. They will have intercom usually if it works anyway. just tell them it's private weigh and they will tell when to pull off. Go park out of the way. Go get your ticket and pay. it will show front axle, rear, and TT.
You should be able to drop your rig out of the way and do a re weigh of just the tow vehicle. Do the math for the rear axle weight and it will tell you your pin weight or tongue weight.
Dont worry about it, you are new and we all are at some time.