Before digital weighing machines were developed in the late 1900s, goods were weighed on weighing machines, also called 'scales' or 'pairs of scales. I remember them from the 1940s, but they were certainly in existence in Victorian and Edwardian times, if not before.
The weighing worked on the simple principle of balancing the goods on one side of an arm against standard weights on the other side. There were, though, different styles of weights and scales for different purposes. The photograph shows scales for relatively light-weight use, for weighing letters to establish the correct postal rate. Probably all Post Offices before digitalisation had something similar.
Shopkeepers needed to work out prices in their heads, but the calculations were not particularly arduous because it was normal practice to sell in simple fractions or simple multiples of a pound (or whatever was the appropriate unit of weight for the goods).
It was necessary for the scales to be set to balance properly, so that the shop was not seen to be selling under-weight. Equally shopkeepers would not want to be giving away more than they were charging for. So there was an arrangement on all scales whereby a small weight could be moved slightly one way or the other along the arms of the scales to balance up each side. Unfortunately it tends to be rather difficult to see in the photos.
In practice, shop scales were normally too rough and ready for perfect balance, or maybe the shopkeepers had to work too fast to bother. Either way, it was normal practice for them to give customers the benefit of any doubt by putting just too much on the customer's scale pan and giving the customer time to register that this was happening. Presumably there was a skill in making the 'just' as small as possible.
Weighing machines based on extending or contracting springs were not used much, if at all, in shops in the early 1900s. They were probably not thought necessary as customers always bought standard weights at standard prices per pound or per ounce. However scales based on springs were in general use in shops by the 1950s.
The following photos show more types of scales. All are designed for specific purposes, with their pans specially shaped for efficient use.
Most of these photos of scales also show the weights that were used with them - generally round brass or iron ones that stacked for tidy storage.
There were also heavy duty weights that incorporated handles for lifting, and there were extremely delicate weights which were used by pharmacists for making up prescriptions. The delicate weights were stored in air-tight boxes to avoid contamination from the air. They were shaped with 'necks and heads' so that they could easily be grasped with the tweezers that were stored with them to prevent greasy fingers from altering their weights. The following photographs were taken at Milestones Museum in Basingstoke.