The way the law is written is to give a discount to primary residences to help people keep cost of living down. The cost is then passed onto all other properties pay the full rate, not just 2nd homes, all land and commercial properties pay the full rate. The logic is that if you have enough money to own a 2nd home you can afford to pay more in taxes.

Personally I think perpetual property taxes are immoral.

If you don't agree with the county assessment and they deny your appeal you can still appeal to the state.