Why the rotor core losses are very tiny compared to the stator core losses in an induction motor?
The rotor is rotating at near the frequency of the rotating field produced by the stator, so it only actually sees an alternating field at a frequency proportional to the slip (In the absence of harmonic distortion), maybe a few percent of line frequency.

The stator has a field at the line frequency and that is very much higher then the slip angular frequency, since the losses are proportional to frequency (to a first order) you would expect the rotor losses to be much smaller then the stator losses all else being equal.