“fair weight.” The literal Hebrew is an idiom, “a stone of peace,” but that would not make sense in English. A “stone of peace” was a just and true weight.
In the ancient world most goods were exchanged by using a balance and stone weights. A merchant would have a balance, which was usually a stick with a cord in the middle that he held on to, and on each end of the stick was a cord that went down to a pouch or pan. (The iconic image of “Lady Justice” that appears in many courthouses in the USA is a blindfolded woman holding out a balance).
Traveling merchants would carry the balance with them, and also carry their “weighing stones,” which they used in buying and selling, which were stones of different weight (1 shekel; 5 shekels; 20 shekels; etc.). The weights that were used by merchants in Old Testament times were usually made of stone; metal weights were not common.
When buying or selling, the merchant would place the item being bought or sold, for example wheat, in one pan and his weighing stones in the other pan, and adjust either the amount of wheat or the stones until the wheat and stones “balanced,” at which point the weight and thus value of the wheat was known.
Unscrupulous merchants often kept different stones in their bag that only they could easily tell apart, stones that were a little heavier for buying and stones that were a little lighter for selling, so that they bought a lot and sold a little. But that kind of dishonest dealing is an abomination to Yahweh. Yahweh commanded traders to use honest weights and measures, which gave people what they deserved in a business deal (Lev. 19:35). In ancient Israel, it was the job of the Levites to maintain the standard weights and measures that merchants could use to standardize their own weights and measures so people got a fair deal.
In modern times “balances” have been mostly replaced by “scales.” A balance is accurate, but it took considerable time and tweaking to get both sides of the balance to be the same weight so it would balance out and be level. Besides that, sometimes a person would have to buy or sell a little more or less than they really wanted because the stone weights were set amounts and the person had to add or subtract a little wheat to make the balance level out. Today, stores use scales for weighing that use different ways of producing known resistance to weight, for example, many scales use springs. Grocery stores use scales to weigh meat and vegetables. In scientific terms, a balance measures relative mass, comparing one object to another, while a scale measures the weight of an object using resistance to gravity. The subject of balances and scales can be somewhat confusing because often “balances” are called “scales,” but technically they are not.
There was enough dishonesty in ancient dealings that God spoke about being honest several different times (cp. Deut. 25:13-16; Prov. 11:1; 16:11; 20:10, 23; Ezek. 45:10; Hosea 12:7; Amos 8:5; Micah 6:11).