A query on the non-uniform quantization
To make it more clear, I suppose your question is


  Why it is said that the compressor gain at low input amplitudes is higher, while the step size of a nonuniform quantizer is small in that region. Similarly, Why it is said that the gain of the compressor is higher for high input amplitudes, while the step size is larger for those inputs.


First, notice that nonuniform quantization is used to improve the average SNR by adapting the quantizer to the source probability density function. Of course, when the source pdf is not uniform (e.g. when it is Gaussian), then uniform quantization is not a good choice. To better understand it, assume that you want to quantize a Gaussian source into $K$ levels. Let's first assume we have a uniform quantizer. One way to reduce the distortion caused by qunantization is to increase the number of steps ($K$). Increasing $K$ means the step size is reduced which eventually leads to a higher SNR (finer quantization). Increasing the number of levels means that the total number of bits to represent each sample is increased. For instance if we have 256 levels we need 8 bits to represent each level. But for 1024 levels we will require 10 bits.

Now in the above example assume that we want to work with a fixed $K$ (e.g. 256) and improve the SNR. To do this, notice that a Gaussian source is more likely to produce samples around the mean. So for example, a zero-mean Gaussian source is very likely to generate values close to zero. So we allocate smaller step size in the area around zero, and instead make the step size larger at the tail of the pdf (where it is less likely to happen). So technically, we quantize with a smaller step size on average (but without increasing the number of levels).



Any scalar nonuniform quantizer can be implemented by using a chain of 

1- A compressor: a memoryless monotonic nonlinearity $G$

2- A uniform quantizer

3- An expander: inverse of nonlinearity $G$

In your example, the nonlinearity has a large gain at the origin (the characteristic function is steep) while it causes some sort of saturation effect at large amplitudes. But this gain is applied on the input signal not on the quantizer. Still the result should be quantized by a uniform quantizer afterwards. Although it is a uniform quantizer, but the preliminary change caused by the nonlinearity $G$ and then $G^{-1}$ makes it seem as if different step sizes are used: The low amplitude bins are magnified first, then there is a uniform grid, then they are compressed. They seem as they are quantized by a small step size. Something similar also applies to the high amplitude bins, except they are compressed first, then they are expanded. So the overall result is equivalent to the effect of a large step size.