The correct answer is D) American Bureau of Shipping. The periodic weight testing of a vessel's cargo booms is typically conducted by a recognized classification society, such as the American Bureau of Shipping (ABS). As a classification society, ABS is responsible for setting and enforcing standards related to the design, construction, and maintenance of marine vessels, including the periodic testing of cargo handling equipment like booms. This is in accordance with the regulations and guidelines established by the International Maritime Organization (IMO) and adopted by the U.S. Coast Guard. The other options are incorrect because the National Cargo Bureau, the Society of Naval Architects and Marine Engineers, and the U.S. Coast Guard are not directly responsible for conducting the periodic weight testing of cargo booms. These organizations may have other roles in the maritime industry, but the primary responsibility for this specific task lies with the vessel's classification society, such as ABS.