From an evolutionary perspective:
We produce a tan (increased melanin) because our vulnerability to UV damage creates an evolutionary disadvantage. This evolutionary disadvantage is so pronounced that in regions with elevated UV exposure (tropical regions), just being able to tan was inadequate, thus, we are born with a built-in tan (dark-skinned races).
I interpret this to mean that once you have been exposed to enough sun to produce adequate amounts vitamin D3, a surplus amount of UV beyond this offers no survival advantage and an excess leads to a survival disadvantage.

I would define "excess amount" as the amount to produce a marked tanning response, given that our bodies are mounting a protective response to a UV threat.