This project was on one of Discovery Channel's extreme engineering shows so I can confirm that it's true. As for figuring out the weight, you need only calculate the weight of the water. If I recall correctly, a ship's weight is given in tons of water displaced. Thus a ship of 16,000 tons displacement, displaces 16,000 tons of water. So the weight on the bridge will remain constant even when a ship passes over it because an equivalent weight of water is pushed out of the way.