You have two options, follow the repair requirements in the National Board Inspection Code, or follow the requirements in one of the API Codes.
Since I am most familiar with the NBIC, I can tell you that thinning can be repaired by either weld overlay or a flush patch plate. Regarding weld overlay, this can only be performed on the side of the vessel that has the wastage. So, if the wastage is on the ID surface, you can weld repair from the ID side of the vessel. If this is not possible, you need to use a flush patch plate.
Have you used API 579 to evaluate if you can leave the thinned area?