Dropping an anchor from a boat

Imagine the anchor is hanging from the bottom of the boat, dangling mid-water like this:

(There is no difference between the anchor hanging in the water and sitting in the boat, since the system boat + anchor weighs the same either way.)

The water level depends on how heavy the anchor is. If you make the anchor heavier, it pulls the boat down further, pushing the water out of the way. This water goes out to the sides and raises the water level a bit. If you make the anchor lighter, the boat rises up some, leaving a gap. Water rushes in underneath the boat, and the water level goes down.

Imagine making the chain longer until at last the anchor starts to rest on the bottom of the tank. Since the bottom of the tank is supporting the anchor, it doesn't pull down on the boat as much. From the boat's perspective, it's as if the anchor got lighter. Thus, the boat rises and the water level falls.

We must assume that the anchor is more dense than water, but that is all. If you wanted to calculate how much the water level falls, you would need to know the density and weight of the anchor.