There is no threshold for harm*. It's a cost:benefit consideration. From a cancer/aging perspective, any amount of UV exposure is bad. Tanning is a consequence of DNA damage. If your skin gets darker from sun exposure, you see evidence of your skin cells reacting to increased DNA repair signals. Malignant transformation/senescence is a stochastic event of course, but age markers pretty much suffer in a dose dependent manner.
* Of course exhausting antioxidant capacity will greatly increase damage at a certain point. I am not exactly sure if UV light can cause single strand breakage by itself, or via ROS, but antioxidants are no "shield" in any case - more like a minefield.