Microwaves Heating

Thought Experiment:
If the microwave produces the same amount of radiation for a particular setting, is there a threshold mass such that below a certain mass there is no change from the amount of stuff you put in and the temperature it comes out at?

I imagined microwaves working by producing a set amount of waves that filled the cavity of a microwave - and below a certain volume / mass amount some of the waves would not interact with the material to be heated simply because there was no matter there.  (Thinking of placing a thin disk in the microwave vs. a tall cylinder of equal volume - I would expect the tall cylinder to come out hotter).

Experiment:
I looked at the temperature change of different volumes of water (in the same 2 cup Tupperware measuring cup) for the same amount of heating time (1 min).

As you can see, the temperature change is lograthmic as a function of volume. For the amount of water I was adding, I did not expect to see such a dramatic change. I guess my microwave is wimpy. Look at energy added to the water (from Q=m c deltaT) as a function of water volume.

Linear - does that make sense? Say I have an logarithmic function, T = -27.4ln(V) + 431.2 (the fit for the change in temperature) and a linear function, E = 1057 V + 24285 (the fit for the change in energy). I calculated E as Q = mcT=rho*V*C*T, so then I could write the following: E=rho*V*C*(-27.4ln(V) + 431.2) =? 1057 V + 24285. But the V's in the logarithmic expression for E don't cancel into a linear term, so I have the wrong form for either the change in temperature or the change in energy.

Extra special prize for any suggestions.

And I still haven't answered my original question.