When I use Color Tuning on gray tones I get a very small circle of available range of change for this tone. Why?

Color Tuning is designed specifically not to change neutral tones. The closer to white point your source color is, the smaller range circle of target color you'll get. Color Tuning is intended to fine-tune only more or less saturated color tones.

Use White Balance to change gray tones first, then use Color Tuning to fine-tune the other color tones.