My experience with microwave ovens seems to indicate that cooking time vs. power is not a linear relationship; i.e. cooking something at half power for two minutes produces very different results than cooking the same thing at full power for one minute. Also, food mass vs. power level vs. time does not appear to be linear, judging by the directions printed on food boxes, where heating twice as much food calls for cooking it less than twice as long. So what are the relationships?
Unlike a conventional oven, a microwave doesn’t heat all of the food. It only heats certain materials like water and certain sugars and fats. Cooking at half power actually doesn’t cook at half power. It cooks at full power but turns the power on and off so that it is off half of the time. This is going to allow more time for the heat to transfer from the materials you heated to the other materials in the food.
You’re not going to get one formula that you can use. A cup of water, for example, is going to have an almost linear relationship, because the water is uniformly heated by the microwaves. Other things, as you’ve discovered, are much less linear. It depends on the mixture of materials, how much they absorb radio waves, and how quickly they transfer heat via conduction.
This is not always true. Higher-end ovens often do actually modulate the output power, rather than change the duty cycle. In those units, 50% power really IS 50% power, not 100% power delivered half the time and 0% the other half.