Then take the total weight and divide it by the distance from the center of axles to the coupler and multiply this number by the distance from center of axles to each axle.
After that, add the number to the to the weight opposite of the tongue weight to the axle towards the center of gravity and subtract it from the weight on the axle farthest from the CG. The problem with that is when the axles are centered on the CG, the weights don't equal each other and the total weight.
In my mind it makes sense that if the CG is directly over the center of the axles then there will be zero tongue weight and the the total weight should be evenly distributed between the axles. As the CG is shifted more towards one axle or the other, then the weight will be differing between the axles, with more weight being applied to the axle closest to the CG and less being applied to the one farthest. With this in mind the tongue weight would begin to be positive or negative at a slower speed than if there was only one axle. I just can't figure out how this changes once another axle is in the mix. It makes sense that the tongue weight will be lighter than with a single axle. I have tested this same formula on both a finished single axle trailer (with a resulting actual tongue weight of 232 lbs. and the formula at 238 lbs.) and a tandem axle trailer, but this time the result was (actual weight of 284.5 lbs and formula at 326 lbs.) So with a difference of 41.5 lbs there should be close to equal weight placed on each axle and this is with the CG being 4.507" ahead of the front axle. As to reverse engineering this formula to come out to being even closer to the true weight, I am at a stand still. Attached are the details of the trailer that was actually tested.
The weight on the jack was 284.5 lbs and the jack is 125.25" from the center of the axles. The total weight is 1,920 lbs.