I found the following lines from the Atmel documentation:
"The equivalent series resistance (ESR) is an electrical representation of the
mechanical losses, and at the series resonant frequency, fs, it is equal to R1 in the
electrical model. The ESR is a very important parameter, and can be found in the
crystal datasheet. The ESR will usually be dependent of the crystal’s physical size,
and small crystals (especially small SMD crystals) typically have higher losses and
ESR values than larger crystals.
Higher ESR values will load the inverting amplifier more, and too high an ESR may
cause unstable oscillator operation. Unity gain will not be achieved, and the
Barkhausen criterion will not be fulfilled"