The problem of getting your team field bridge to behave like the ones you're going to see in competitions is a combination of statics AND dynamics. *just like life*

If you position some weights on the other side of the fulcrums so that the battery balance test is passed, you will be dealing with the static difference of your bridge. You should be able to figure out some things about how to deal with bridges, like how hard to push on one edge to get it low enough to drive onto, for instance.
If you want to practice balancing on your bridge, the rotational inertia about the hinge points will become important. So the distribution of the weights you applied to achieve the right static balance will be factors in how the bridge reacts to your fast or slow driving back and forth across it. The reason tight-rope walkers carry a pole is to increase their rotational inertia and decrease the effect of small errors in their walking balance.
You can make the bridge behave statically correct by weights of different amounts at the appropriate distance for each. The chance that it will behave dynamically the same as the metal one is yet to be determined. And we haven't even stopped to consider the hinge friction characteristics under varying loads.
