I think I understand the phenomena the OP is seeing and I'll try and explain what I think the symptoms are:
If power is fed to a linear amplifier and it shows 10kW FWD power and (x)W reflected power then you would expect the reflected power to fall to (x/2)W if the drive to the ampliier was reduced such that the FWD power fell by half to 5kW.
But I think the OP is NOT seeing the expected (x/2)W reflected power at half the FWD power. If this is indeed the case then there are valid real world reasons why these symptoms can be observed.
I won't list them all but you could have an issue with linearity at the higher power level where higher levels of harmonics are disrupting (corrupting?) the measurement system in one or more areas.
eg the power meter may have different coupling/sensitivity to harmonics or its detector may be a crude type that suffers high uncertainty when harmonics are present.
The load may be non linear and have poor performance at the harmonic frequencies or it may simply be changing its impedance at high power levels at certain frequencies as it gets hot.
The coupler directivity (and coupling factor) may be different at harmonic frequencies.
The amplifier could be going unstable at certain frequencies and power levels and this can produce all manner of strange symptoms on a basic power meter.
Are you using a Bird model 43 wattmeter to make these measurements? If so, are you using the correct plug-in for the frequency/power range? Are you sure the dummy load is flat across the frequency range of interest (verify by measuring forward and reflected power with the Bird). If you aren't using a Bird and a good dummy load then you can't really trust any of your measurements.
I'm afraid that the Bird 43 'wattmeter' is not a proper power meter for various reasons. It's design is seriously compromised in favour of its versatility and it's arguable that it is technically inferior to a $5 CB power meter for some types of tests.
Basically, don't trust any RF 'professional' who claims/argues that the Bird 43 is some kind of industry standard benchmark for RF power measurement. It most certainly isn't! However, the myths about this meter will go on and on because there is no shortage of gullible hams/owners/techs who 'believe' the folklore/hype about the capabilities of this crude and awful device.