I think you all have it now...
Its all about density. In this case density of the barge and concrete relative to the density of water.
The barge weighs 300 tonnes say, and its carrying 100 tonnes say, of concrete blocks. The barge floats.... so the density of each cubic metre of barge hull volume thats under the water must be the same as the density of each cubic metre of the water it floats in.
Assuming the density of the water is 1 tonne per cubic metre, the barge and its load of concrete is displacing 400 cubic metres of water.
The concrete blocks dont float, as we know their density is far higher than 1 tonne per cubic metre.
Once the concrete blocks are off the barge and into the water, the cubic volume of 100 tonnes of concrete is now displacing far less than the cubic volume of 100 tonnes of water.
So, overall, once the concrete is not being supported by a floating barge, less volume of water is being displaced and the water level in the tank will fall.