Can someone explain how frequency and inductance affects this pair of coupled inductors?
From what I read about coupled inductors, an increase in frequency
  should result in an increase in the voltage across the secondary
  inductor.


That's only true if the RMS current in the primary remains constant and then the output voltage is proportional to frequency because the induced voltage is proportional to \$\dfrac{d\Phi}{dt}\$.

However, you have a primary winding and that winding has inductance and as frequency rises the reactance increases and the current falls with frequency. The result is that you get a constant output voltage with frequency.

Any difference from the theoretical will be down to other components affecting things. Consider your circuit broken down into three reactive components; the leakage in the primary due to imperfect coupling, the secondary leakage also due to imperfect coupling and the transformer representing the fraction of perfect coupling that remains: -