“paid for.” In certain contexts, the Hebrew verb ratsah (#07521 רָצָה) means to “make up for,” “pay for,” “expiate,” and this is one of those cases. This same word occurs in Leviticus 26:34, 41, and 26:43. Keil and Delitzsch write that Israel’s “iniquity is atoned for, and the justice of God is satisfied: [The Hebrew word ratsah] which generally denotes a satisfactory reception, is used here in the sense of meeting with a satisfactory payment, like [ratsah avon] in Lev. 26:41, 43, to pay off the debt of sin by enduring the punishment of sin” (Commentary on the Old Testament).
The sin of Israel has been “paid off,” and thus pardoned, because she received from Yahweh “double” for all her sins. God had said that sometimes sin would be repaid double (cp. Jer. 16:18; 17:18) and in Leviticus 26, God had clearly said that if people behaved like Israel had behaved, they would receive “sevenfold” punishment for their sin (Lev. 26:18, 24, 28). In any case, at this point, Israel had paid for her sin. This verse in Isaiah shows that sin was sometimes thought of in terms of being a debt that needed to be paid, something that was much more fully developed during and after the Babylonian Captivity and during New Testament times. [For a more complete understanding of sin, see commentary on 1 John 1:7, “sin.” For a more complete understanding of the land incurring a debt when the Sabbath years were not honored, see Lev. 26 and the commentary on Lev. 26:34].
“double for all her sins.” The word “double” here could mean twice as much punishment as Jerusalem deserved, but it is more likely that in this context it simply means “an abundance” or “enough.” There is no reason for God to punish Jerusalem twice as much as she deserved.