On large modern ships its actually not the anchor itself that holds the ship from moving, its the weight of the anchor chain that also lies on the bottom. The cleats (they have a name, can’t remember) or spade like bits on the anchor are to keep the anchor from dragging along the seabed, but only in a lateral direction. When the chain lifts straight up, they disengage and the anchor is lifted out of the seabed.
So, to lift the anchor, the windlass only has to lift the length of chain that is off the seafloor, not the whole thing. And due to the magic of gearing, a moderate size motor can lift quite a bit of weight.
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