The weight of sea water really depends on a number of variables, including the temperature, the amount of salt (salinity) and whatever other foreign items may be present, and the depth, thus the pressure.
But to get to the basic answer, seawater, at the surface, on average weighs 1027 kg/m3, or just over 64.1 lbs per cubic foot.
It is more correct to refer to the weight of salt water in terms of density. Salt water has greater density than that of fresh water obviously due to the additional density of salt. Fresh water has a density of 1000 kg/cubic meter vs. an average density of 1027 kg/cubic meter for ocean salt water.