The correct answer is C) draft and beam of the drilling unit. The height of the metacenter above the keel is primarily determined by the draft and beam of the vessel. The metacenter is a point above the center of buoyancy that represents the stability of the vessel. Its position relative to the vessel's center of gravity determines the vessel's stability characteristics. Specifically, the height of the metacenter increases as the draft decreases and the beam increases, which enhances the vessel's stability. The other answer choices are incorrect because they do not directly affect the position of the metacenter. Displacement and deadweight (A) primarily influence the vessel's overall buoyancy, while tonnage (B) is a measure of the vessel's size. Buoyancy and trim (D) are factors that are influenced by the metacenter, but do not directly determine its position.