Have 10,000# digital gauge on the loader lift arms. Multi function, units, tare, net, etc. Weighed logs and 3pt 960# counter weight with a crane scale for reference. Picked up known weights and tried to develop a formula or rule of thumb to guesstimate weight from loader pressure. While individual weights were repeatable, combinations were not. New loads not very close even when using the same lift height and curl. Beyond my calculus skills.
Hay bales are probably more consistent than my loads. Even with the same bale of known weight, how you stick it, raise it, curl it, ground grade will all effect loader pressure. 10-15% error adds up. I understand your effort in providing your customers with the best service.
There are loaders that have weight scales like at the quarry. Some loader operators are very accurate. None sell by that weight that I know of.
So many more variables of quality and quantity i looked for when buying hay.