1759 (in an account of the Battle of Lagos in "Universal Magazine," September), from water (n.1) + log (n.1); the notion apparently is of "reduce to a log-like condition." Compare logged.
WATER LOGGED, the state of a ship when, by receiving a great quantity of water into her hold, by leaking, &c., she has become heavy and inactive upon the sea, so as to yield without resistance to the efforts of every wave rushing over her decks. As, in this dangerous situation, the center of gravity is no longer fixed, but fluctuating from place to place, the stability of the ship is utterly lost. She is therefore almost totally deprived of the use of her sails, which would operate to overset her, or press the head under water. Hence there is no resource for the crew, except to free her by the pumps, or to abandon her by the boats as soon as possible. [William Falconer, "An Universal Dictionary of the Marine," London, 1784]
The verb waterlog (1779) appears to be a back-formation.