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I agree that the bottom will flex up under the box, but for reasons outlined by others. The pressure exerted on the bottom of the aquarium just below the box is less than the pressure exerted on the aquarium bottom all around it. Not because of a buoyant force on the box, because you have removed the mechanism for that force, but because there is "less water" above that part of the bottom of the aquarium. And yes, it will be equal to the weight of the water displaced, but that doesn't mean it's a buoyant force pushing up on the box.
Bill