“weights.” The Hebrew is literally “stones.” For most of history, the weights used by merchants for their scales were stones. Metal was too rare or expensive. The merchants most often had a sack of some kind to carry the stones in. Occasionally they would carry them in the folds of their garment if their weight and number were small.
“are established by him.” The literal is that the stones in the bag are “his work.” The “bag” is the bag that the merchant would carry that had varying weights in it, and it was God who set the standard weights and measures so trade could be equitably carried out. The NLT is more of a paraphrase than a strict translation, but it gets the sense of the verse: “The LORD demands accurate scales and balances; he sets the standards for fairness.” Saying the weights in the bag are the work of Yahweh is a way of saying that He set the standard measures, and He expects people to be honest in their trade. From the standard that God established, the Levites and the king were responsible to see that merchants had accurate weights and measures, but that proved to be an almost impossible task. Since the weights at this time were almost always made of stone, the temptation was great to chip a little off when you were selling something so you did not have to sell so much, and to get a slightly heavier weight when you were buying something so you got a little more for your money.