It's a myth that microwave absorption by water is a resonant process. See Does a domestic microwave work by emitting an electromagnetic wave at the same frequency as a OH bond in water? for a discussion of this.
Light generally interacts with matter by interacting with the electrons in matter. Light has an associated oscillating electric field and this excites oscillations in the electrons in the matter. The electrons may in turn transfer their kinetic energy to lattice vibrations, with the end result of heating the object. Incidentally, black body emission is the reverse of this. Lattice oscillations scatter electrons causing transient dipoles, and these dipole oscillations generate the black body radiation.
How much heating occurs depends simply on how fast the radiation is absorbed, and this is highly dependant on the frequency of the light and the electronic properties of the material. For example silica glass absorbs very little in the visible region while graphite absorbs very strongly. You get similar variations in the microwave region. Water isn't actually a very strong absorber of the 2.45GHz microwaves used in domestic ovens, which is just as well otherwise the centre of the food wouldn't be heated.