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Best way to understand it is to consider how a submarine works
floating on the surface it might displace ψ tons, but a bathroom scale type weighing device would read 0
to submerge it replaces air in tanks surrounding the pressure hull w/ denser/ heavier sea water until it attains the buoyancy state that it wants, usually close to or at neutral buoyancy, here the mass of the enclosed volume of the sub equals the mass of the equivalent volume of sea water, the mass of the sub is still the same as when it was on the surface but x amount of air has been replaced w/ y amount of water and when the weight of the extra ballast water is added in the sub is far more massive but the mass only affects propulsion in that the entire mass has to be accelerated, If a bathroom scale were placed under the sub to weigh it it would read 0, same as the scale would read on the surface where the neutral bouncy state also existed
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