Let me toss this hypothesis into the conversation here. If a gene -- or set of genes -- developed which conferred on a grandfather the ability to recognize his son's sons and favor them over granddaughters in a way that promoted their the son's sons reproductive success, wouldn't the gene(s) keep spreading as long a sons were born?

I think the answer is YES if the gene(s) is/are on the Y chromosome. (Thus, this would not arise with a mother's daughter's daughters.)