When in FL I contacted local DOT office and asked for free weighing. They were more than happy to help. Their cruisers carry portable scales in the trunk.
In TN, I called local trooper office and asked if I could weigh off-side at local I-81 scale. They told me to come by on a specific Saturday and I was able to run through several times to get side to side weights.
I bought a portable scale and weighed several years later and found that my weights didn't really change than much to change the air pressures.
I would recommend a 4 corner weight once. If you can't, I really don't think you will find much air pressure difference on the axle. If in doubt, raise your air pressure 10 or 15 lbs until you can get 4 corner weight.
You really are/should only worry that one tire will be under inflated for the weight on the axle.