It's logical to think that the time it takes a microwave to heat the food would be proportional to the mass heated. But since a microwave is based on dielectric heating, I think that if you increase the mass of food there will be more water, which will heat the food faster (due to thermalization). Is this reasoning right?
Is there an optimal quantity of food to heat and the time it takes?
Good question. The rate of temperature increase scales as the power absorbed by the food divided by mass of the food. So to understand your question, you need to understand how power is absorbed.
There is a finite amount of power in the microwaves being produced. These microwaves bounce around in the metal cage where you put your food, until they come into contact with the food. (Well, some of them will get absorbed in the metal by imperfect reflection, but let's ignore that at first.) Once they get absorbed by the food, they turn into heat. Because they bounce around until they hit some food, the efficiency of a microwave is pretty high, in the sense that most of the power generated in the form of microwaves goes into heating the food, regardless of how much food you have.
So, at lowest-order, increasing the mass will increase the amount of water, but won't increase the amount of power being absorbed by the food. But now, that thing about absorption by the metal comes in. The power absorption will be slightly greater with a lot of food, since the food will be more likely to absorb the microwave before it gets absorbed by the metal. This is a lower-order effect, but it's there.
Of course, then the issue of skin depth comes in. Microwaves only penetrate a certain distance into the food. (Of order an inch, depending on the food.) So increasing the mass isn't really what you want; you want to increase the mass that's within the skin depth. For example, a wide dish of water that's one inch deep will absorb better than a jug of water with the same volume. This is why you want to split apart chicken breasts when defrosting them, for example.
To answer your question, then, the more food you put in, the more efficiently your food will capture the power being produced by the microwave oven. So you will capture the microwave's power better, but you will still heat slower because you have more mass. But this is not a dominant effect, and you might be better off redistributing your food to maximize the surface area.
