<The weight actually carried by the bridge depends only on how deep the operator allows the water to be. (That's also high school physics.)>
I understand what you are saying, but the above sentence is a little misleading. It has been a long time since high school physics, but I still remember that the weight of water is determined by its volume ... not depth.
If the boat floats, it has displaced a volume of water equal to its (the boat's) weight. However, the water displaced is still there so its (the water's) weight is added to the boat's weight. If the water displaced by the boat is released, the total weight will change ... but the DEPTH of the water is only an indirect measure of the total weight. It is the VOLUME of water remaining that counts.
However, if the water is dispersed along the length of the "bridge" from lock to lock, the volume of water remaining on the actual bridge (which does not extend from lock to lock) will decrease proportionally, but the weight of the boat that displaced that water will not decrease, so the bridge will still carry more weight than it would have if the boat was not there, unless the water was actually released from the "bridge" from lock to lock ......
I have confused myself.