I have a toilet flapper with an adjustable float on the chain. As I move the float down the chain, more water is released from the tank per flush. Why is this? How does the mechanism work?
Buoyancy holds the float afloat. Suction holds the flapper down.
When you break the suction, the float can do what it's been trying to do the whole time: get to equilibrium, which is the top of the water level. Only when there's enough chain hanging will it lower the flapper down to where it seals.
Once it seals with even a tiny amount of water and has suction again, you'll have to push the handle down a lot harder than the float is trying to lift; the float only has enough buoyancy to lift the flapper valve, not break the suction.
The height of the float determines how much water can be left over in the tank before it re-seals. The less water left in the tank, the more water down the drain.
Pushing the float down the chain makes the distance between the float and the flapper less, therefore the same is true of the distance between the water level and the flapper. That means more water is released before the flapper is lowered into its sealing position.