Why does an overcompensated oscilloscope probe give spikes higher than the input voltage?
It is a resistive voltage divider in parallel with a capacitive voltage divider:

The output is compared with 1/10 of the input (so, it is not above the input):

The smaller capacitor at the probe is adjusted to match the voltage ratio determined by the resistance of the 10x probe (9M) and the oscilloscope input (1M).
EDIT: to address your comment on frequency response
As for the frequency response, considering only these characteristics and not the others that go beyond your question, you can consider the 10x probe as a voltage divider that deviates from its DC ratio as frequency increases, if not compensated properly.