As you increase the supply voltage, you start to reach H (magnetic field strength) field levels that cause the magnetic core to saturate more.
The effect of saturating the core more is to open up or expand the BH curve and, the impact of doing so means that you lose more energy (disproportionately) in what is called hysteresis loss. Here is a picture that might help you understand: -
Hysteresis loss
At moderate H fields (the blue curve above), the area enclosed is quite small but, as you increase the AC supply voltage, saturation effects cause the area enclosed to become disproportionately bigger and this means more significant losses.
Hysteresis loss is worse at higher supply voltages because you expend more energy in reversing the magnetic field each AC cycle. It's all down to what is called the remanance magnetic field - that is the field remaining in the ferromagnetic core when H field is backed down to zero. This remanance is the value on the Y axis when H is zero and, as you should be able to see on the picture above, is usually quite small for moderate H values.
See also Magnetic Coercivity; this wiki page also shows the widening and broadening effect of the BH curve as greater fields are demanded (by higher primary voltages): -
