the rotor interacts with the stators thru a magnetic field -- more load causes stronger field from stators which causes more resistance for the rotor to oppose (=more torque opposing the rotor)

As I remember, the fixed stator windings in the casing generate a standing field, and the rotating coils of the rotor couple energy out of this field through the torque provided by the engine. Slip rings transfer the induced rotor current (AC) out of the generator. The field (stator) current is increased for heavier loads and decreased for lighter loads, to overcome copper losses, maintaining output voltage regulation. Note that the engine speed must remain constant, or the frequency of the generated AC will deviate, so a rev. governor is required for the engine.

There's a couple of things to consider. Suppose that the generator is being driven by a constant-speed source (e.g., a turbine with a speed governor). The generator would produce a voltage (specifically, it's "open circuit voltage" for that speed, but no current would flow, and no electrical power would be produced. Only enough torque is being transmitted down the generator's input shaft to overcome various parasitic losses such as bearing friction, windage, and eddy current losses. Suppose that instead of a constant-speed source, we insist on a constant-power source. What would happen is that the generator's speed of rotation increases until these parasitic losses grow large enough to absorb all of the applied shaft power. Again, no electrical power is being produced. This is much like pressing the gas pedal in your car when the transmission is in neutral -- even a small amount of gas causes the engine to race madly, yet no useful power is being produced. All of the input power (i.e., the expansion of burning gasoline vapor in the cylinders) is being absorbed by internal friction losses (pistons scraping the cylinder walls, bearing friction, windage losses in the crankcase), and external losses (fan blades, power steering pump, A/C compressor).

If the load is increased the resistance at the output reduces and without modification the voltage across the output would fall. Two ways to compensate, increase the speed of rotation which would affect the frequency of any AC output or increase the field current, which strengthens the magnetic field and increases output power at constant speed. If the load is decreased the opposite is the case starting with the resistance at the output increasing and the voltage at the output tending to rise.

5-24-2017 It takes several days to teach the motor-generator effect. Here is a free course in the basics: http://www.phy.davidson.edu/instrumentation/NEETS.htm