This is simply a matter of force balancing. The only forces on each magnet are gravity and the magnetic repulsion from the neighbors.
The top magnet must be repelled from below with a force equal in magnitude to the force of gravity on it.
The next magnet down has not only its own weight pushing down, but the weight of the one above it as well. This is an example of Newton's Third Law: If the second-from-the-top magnet is pushing on the top one, then the reverse must be true with an equal force. Thus this second magnet must be pushed up with twice the force required to levitate the top magnet. It reaches equilibrium closer to the repelling magnet below.
This trend continues, with the $n$-th magnet bearing about $n$ times the weight of one of them. The spacings decrease as a result. Note that the force of repulsion depends strongly on distance, so the space below the $n$-th magnet does not have to be $1/n$ the spacing below the first magnet for equilibrium to be achieved.