I have a loss of lows (bass) when I turn the volume down, the tone gets thinner. At 7 it's clearly thinner than at 10. I have a Hagström III with three singlecoils. How do different Pot sizes (250 k, 500 k or 1 Meg) affect this behavior?
If you have a treble bleed cap on the volume controls, it is a suspect. Sometimes the value used is too high, when combined with your cable and amp combination. Its function is to cure loss of treble as you reduce volume (due mainly to the cable acting as a capacitor, like in a treble-cut tone control), but if it is too effective, then it preserves too much treble, making the tone too thin at reduced volume. Its easy to improve, if you can find the relevant circuit diagram for the guitar.