I don't know the "proper" way to weigh the axles, but using your procedures with a tongue scale is probably not very accurate.
Here's how I would do it:
Go to a truckstop that has a CAT scale. A CAT scale has 3 or 4 pads for weighing various axles on the truck and trailer(s).
Place the trailer on the scale so the rear axle of the trailer is on a scale pad by itself. Weigh the rig and don't worry about any of the scale pads except the one with just the rear trailer axle on it.
Pay for that weighing, then pull around and weigh the rig again, but this time with the front axle of the tow vehicle on one pad, the rear axle of the tow vehicle on a different pad, and both trailer axles on the third pad.
Subtract the weight of one trailer axle on a pad from the weight of both trailer axles on a pad. That will tell you how much difference in weight is on each of the two trailer axles.
That will give you a much more accurate indication of the weight on each axle.
The trailer may be designed so that the tandam axles have approximately the same weight only when the trailer is loaded, and with the payload properly distributed on the trailer.
Grumpy ole man with over 50 years towing experience. Now my heaviest trailer is a 7,000-pound enclosed cargo trailer, RV is a 5,600 pound Skyline Nomad Joey 196S, and my tow vehicle is a 2012 F-150 EcoBoost SuperCrew.