If you are careful and understand what you are doing, you can very accurately determine the tongue weight of the trailer using the bathroom scale/lever method. You cannot accurately determine the total weight of the trailer this way, you can only estimate that the tongue weight is about 10% of the total weight.
Have you looked through local ads for used trailers getting parted out, or maybe called around to local junkyards? Maybe you can find a trailer that got a little busted up that has a modern axle with brakes wheels and everything, that you can just swap out?
I suggested the method COULD be used on the end of the axles to get the "on the ground" load.
Probably only do one front and one rear wheel and it would be safest to do it at the axle flange, e.g. not on anything that spins around (-:
The 10% rule is ONLY a rule of thumb, you can't work backwards from tongue load to trailer weight.
In my opinion 10% is a minimum, closer to 15% is my preference for trailer stability - as long as the tow vehicle doesn't sag too much, then you are into a whole 'nother set of answers than bring further questions.