Those responsible for maintaining roads ( eg local/national governments) specify the maximum loads that each axle of any vehicle using them may bring to bear on the road surface. This is presumably so that the road has a reasonable life span. This is a static evaluation of the theoretical load supported by an axle in a particular configuration. Knowing the disposition of the axles relative to the centre of gravity of the mass supported (vehicle plus payload) allows you to work out the way that mass is distributed among the axles, treating the problem as '2D'. In other words assuming the left and right wheels on the axles are equally loaded.
Axle load for a road vehicle can be measured simply by driving the vehicle over a commercial weighbridge and weighing one axle at a time. The results will depend on how the load is positioned on the vehicle. The quantity of fuel carried, among other things, will affect the overall result.
Axle load for a rail vehicle can be done in a similar fashion, though the equipment is rather more compact than a commercial weighbridge. It is portable and can be slipped beneath the wheelset.