> Both parties can get 3 times as much money as they did previously.

Increased productivity shifts the supply curve which will (unless demand has zero elasticity, which is unrealistic) lower the market price of the good. So tripling productivity does not triple the amount of revenue per hour worked.

> Why does one party get 10x and the other party get 0.7x?

Because the people purchasing labor (capital) are able to get the labor they need at that price. Automatic weaving machine operators are trainable, and if they were getting paid 3 times what weavers were paid then people would rush into that space, driving down labor prices—in other words, the supply of automatic weaving machine operators has high elasticity. The demand for automatic weaving machine operators (i.e. the supply of factories full of automatic weaving machines) has much lower elasticity, so capital (demand for labor) gets most of the economic surplus.