to weigh: to set an amount on a balance to measure its weight, and so to weigh out silver as payment
The picture behind this word is always the balance scale. Before coins existed, precious metal was money, and every payment was literally a weighing: pieces of silver were set on one pan until they matched the agreed weight. So the one verb covers both jobs a scale did, finding out how heavy something is and handing over a measured sum of silver.
In its plain sense it weighs anything measurable. Absalom's yearly haircut is weighed at two hundred shekels, God is pictured weighing the mountains and hills on a scale, and the same image turns inward when Job asks that his grief be weighed against the sand of the sea, or that he himself be weighed in an honest balance.
In its everyday commercial sense it is simply the word for paying. Abraham weighs out four hundred shekels of silver for a burial plot, Jeremiah weighs out the price of a field, and thirty pieces of silver are weighed out as a wage. Hebrew also has words that lean more toward gauging or leveling a measure (תָּכַן, פָּלַס); this one keeps its feet in the marketplace, where weighing and paying are the same act. The name of the shekel comes straight from this verb, since a shekel was first of all a weight, not a coin.