Maybe start over GenX. Do a search on Ron Gratz and his method of weighing. When you drive onto the CAT scales the front axle goes on the forward pad, the read axle goes on the center pad and the trailer on the back pad. As you pull onto the scales drive ahead and as you think you are on the front pad check your rear view side mirror to confirm that the back axle and trailer axles are on their respective pad. WD set the way you normally have it.
Best to do this in camping configuration. Wife, dogs, kids, stuff in the back of the tow vehicle with full tank of gas, trailer with full propane, full water and little in the grey and black tanks.
I jump out of the truck, high five the call button and immediately jump back into the truck with the door open. Tell them that it is a first weigh, private vehicle and wait until they say they are done and to come in. Go in and pay the first weigh ticket. Now comes the fun.
Go back for the first re-weigh. Take the torsion off of the WD system so it is loose. High five the call button and get another weight. Drive off the scales and go pay.
Disconnect the trailer and weigh just the truck. By now the wife, kids and dogs are ready to go home or kill ya. High five the button, get quickly back in the truck and drive off an pay when they are done.
Now if you have a friendly CAT scale operator and they are slow I go in and talk with them before I start this dance. I tell them I would like to do 3 - 4 weights without moving from the scale. I give them my credit card. Now I pull on, and in the case of a ProPride I set it for maybe 5 inches, get a weight. Jump out and move the jacks to 6 inches. Get another weight. Do it again at 7 inches and the fourth time I run the WD down to the loose position. So 4 weights in maybe 10 minutes.
Lots of Back and forth. Key is to get back into the truck after you high five the squawk box. Or at least stand next to the drivers door. Consistency.
Drive off and drop the trailer and do one last weighing with the tow vehicle.
Now go pay and collect your 5-7 tickets. Keep notes of the sequence and label the tickets before you forget.
With a ProPride/Hensley and cooperation of the CAT operator this can be done quickly. With other hitch types might be more difficult but you get the idea.
CAT as you found out charges $10 for the first weigh and $2 for anything subsequent within 24 hours at the same scale.
And here's Ron's calculations in an excel file that you can crunch all of the numbers. This is for my Sierra 2500 and an FC 25 rear bed.
1_Cat Calc Sierra 2500 7-23-14.xlsx