Here "carried our sins" means he suffered the punishment for our sins. Alternate translation: "suffered the punishment for our sins in his body on the tree" (See: [[rc://en/ta/man/translate/figs-metonymy]])
This can be stated in active form. Alternate translation: "God has healed you because people bruised him" (See: [[rc://en/ta/man/translate/figs-activepassive]])