I wouldn't expect that you would be asked to pay extra for a new port. As I understand it, you would never be charged more in port fees than what the original booking called for. And you MIGHT get a refund for the missed ports.
Here's what was explained to me the last time we missed a port.
Port charges go up and down. From the moment you booked, if the port charges of any given port go up, you are not charged extra to cover that. Similarly, if they go down, you don't get a refund. You pay exactly what the initial booking required. In the months between when you book and when you cruise, port charges may have gone up or down, but you aren't asked for more money or given a refund.
Once the cruise starts, if a port is missed, they look at the total of the port charges for that cruise. Maybe some went up, so you don't get a refund for the missed port. But maybe the total went down, and in that case you get the port charge back for the one you skipped.
Port charges also vary by what country you are from. Say you are traveling with friends from France. One country, call it Q, charges French citizens more port tax than American citizens. Your cruise doesn't call on that country because of bad weather. The port charges for all the other islands have been going up and down since the initial booking. Some went up a little, some went down a little. The total may have gone down enough that the French citizens will get a refund for the missed port but the American citizens won't. And Australians might get a refund but less than what the French get.
So you will never get charged extra if port taxes go up, and you won't get refunds if port taxes go down, but if a port is missed you MIGHT get some port taxes back as OBC on your shipboard account. And if you ask other passengers, you might find that the amount they are refunded is different from what you get, or perhaps you get a refund and someone else on the same cruise doesn't.