Battery C rating won’t make any difference, the battery doesn’t push correct to the motor, it supplies current based on the MOTOR load, more load (e.g. bigger/pitchier prop) means the motor draws more current. You can plug a motor into a Tesla battery and if the voltage and motor load is the same, it will simply draw the same current.
Adding voltage will cause the motor to turn the prop faster, making more power but also increasing the motor load, since the drag on the prop will be greater as it spins faster.
Adding more battery weight and making the plane fly faster and more aggressively will add much more strain on the wing loading, hence snapping.