There were several reasons why God asked particularly for the value of half a shekel as a penalty. As they committed their sin, the worship of the Golden Calf, in the middle, that is the half of the day, so they were to pay half of a shekel; and, furthermore, as they committed their sin in the sixth hour of the day, so were they to pay half a shekel, which is six grains of silver. This half shekel, furthermore, contains ten gerahs, and is hence the corresponding fine for those who trespassed the Ten Commandments. The half shekel was also to be an atonement for the sin committed by the ten sons of Jacob, who sold their brother Joseph as a slave, for whom each had received half a shekel as his share.
Why the Israelites Worshipped a Shiny Golden Idol
Legends of the Jews 2:141