The correct answer is B) Inspect and weigh the cartridge. During the annual servicing and inspection of a dry-chemical cartridge-operated portable fire extinguisher, the most routine action is to inspect and weigh the cartridge. This is required by regulation to ensure the cartridge contains the proper charge and has not been tampered with or lost pressure. The other options, while potentially part of the inspection process, are not the most routine or commonly performed actions. Checking the pressure gauge, pressure testing the discharge hose, and replacing the dry chemical are also important, but not as fundamental as verifying the cartridge's integrity during the annual service.