Do you think chickens are smart enough to start laying somewhere else, just so they can eat the eggs? I'm very curious how this all works out. It's for sure, you love your biddies!
I don't have any documentation for this, but I've seen people mention in passing that double yolkers from established layers can indicate an overweight hen. Maybe it's your egg eater :hu
Then again, I don't know if two months is considered an established hen or not.