Suzkat,
These fouled anchor flasks were made by NP Ames for the US Navy to be used with the Ames M1842 Navy pistol, also known as the Ames Navy Box Lock. They were also used with the Jenks Navy carbines and rifles purchased by the US Navy in the 1840's. The WAT marking was for an inspector, William A Thorton; the P was for James S. Palmer, USN, also an inspector. They were in use up to and through the Civil War.
These are truly hefty, solid flasks. My father, US Navy WWII in the Pacific, collected Civil War US Navy sidearms, with me tagging along at his side. When he passed, I inherited his collection.
Bill