Densities are measured over a range of temperatures, usually, and for convenience, at the temperature at which the fuel is stored.
The value is then corrected back to 15oC, which is the reference temperature used by most excise authorities. The correction is made by use of standard tables, derived from a large number of fuels representing world-wide fuel availability.
Knowledge of the density of fuels is needed for quantity calculations, its value is also needed for the selection of the correct gravity discs (or rings) on conventional purifying centrifuges.
Of all the contaminants in marine fuel oils water is the most common. The actual level is normally very low, 0.1-0.2% volume is typical. Ingress of water can be traced to a number of sources, among them I recall tank condensation and steam heating coils leakage.
Since marine fuel oil is purchased by the shipowner to produce heat for conversion into work, a value of its "specific energy" is needed. This specific energy (gross and net) is estimated from formulas based on the density of the fuel, corrected for any sulfur, water and ash that may be present.
Other characteristics of importance (beside price) are fuel stability, compatibility, sludge formation tendencies, pour point and, of course, viscosity.