Don’t know anything about fires or airplanes. But I know a bit about physics.
The additional weight of the water in the plane requires the exact energy required to scoop it up and raise it up to whatever height the plane wishes to raise it to. These are called kinetic and potential gravitational energies.
Due to conservation of energy, the planes engines must supply this energy (by burning fuel).
Conversely, when the plane drops the water, it becomes lighter and there is less potential energy so the pilots would have to apply progressively less thrust.
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