The point of this exercise is to take small sections of the Morse potential and see how they compare to the potentials we know. For low values of n (energies less than around -0.8 in the diagram) the potential looks like this:

As you can see, this looks a like a slightly lopsided harmonic oscillator potential. Since the energy level spacing depends on the shape, we would expect the energy levels to be spaced about evenly (as with the harmonic oscillator). Since the anharmonicity (fancy word meaning "not shaped like a harmonic oscillator") makes it look a little like a hydrogen atom potential, we'd expect levels to get a little more closely spaced.

At higher energies, the Morse potential looks more like a hydrogen atom potential. For the hydrogen atom, we know that the energy levels get more closely packed together, so we would expect similar behavior in the high-energy Morse potential.