This has several potential uses, the most obvious being a platform for a treasure chest. Inhabitants can remove the chest without disabling the trap by lifting it straight up; adventurers are more likely to push or drag the chest, shifting the plate and setting off the trigger.
A variation of this is to make an entire section of floor into a large equilibrium trigger. If the plate is large enough, even moving a few feet from the center might not set it off, at least not right away; trying to reach the door, on the other hand, activates the trigger. Dwarves will be able to notice the slight slope as the floor tilts; others might not notice until the the tilt is enough to activate a lever. Options for this would be to drop a party in the center of a room via a chute or to have a large hidden catch or support under the floor in front of one entrance, so that adventurers can reach the center but not an exit on the opposite side. Avoiding this might involve jumping to the center of a room, then to the doorway, assuming the door is open.
One gimmick that pressure triggers and compression triggers don't share is that each tilt direction can have its own, separate mechanism, which means different traps can be triggered depending on which direction an object moves across the balanced platform. A floor with a balanced platform might trigger portcullis traps for individual doorways, based on the direction an adventurer is moving towards.
Equilibrium triggers are detected in the same way as pressure and compression triggers. Methods to disable them, aside from jumping over or into the middle of floor triggers, involve using multiple objects to keep the platform balanced; for example, if adventurers notice a floor beginning to tilt, they can split up and move to separate corners in an attempt to escape the trap. If the ceiling above a trigger is low enough, two or more braces can be used to prevent the plate from tilting.