Why does a block of wood or cork lose more weight in water than its total weight, when totally immersed in wat?

It does not lose any weight. It displaces an amount of water equal to it's volume. Since it is less dense than water, there is a net upward force from the water. When the block is floating, it displaces an amount of water equal to it's weight, so the net force is zero and the block neither rises or falls.