This is easy to prove. Fill a 5gal bucket with tank water, put the filled bucket on a scale, get the reading, now put in a large fish. Does the weight on the scale increase?
As said before, internal forces such as buoyancy caused by the displacement of water would not be registered by an external scale set up to measure the external force of gravity on the whole system. If you add mass to the aquarium, then the total mass and hence the total weight will go up by that amount. Suppose you were standing on a platform scale with another person and the total of your weights was 240 lb. Then, still standing on the scale you lifted the other person so that they were no longer in contact with the scale but being held up by you (this is like the buoyant force on the fish). What do you think the scale would read now? Any other physicists want to chime in? I am one.If you had your aquarium + contents on a scale and the weight shown was 240 lb, and then you added a 1 lb fish, the scale would then read 241 lb,. Buoyancy is an 'internal' force between the fish and the water and has nothiing to do with the pull of gravity (ie. weight) externally on the whole works.