No, you won't have to pay again if you're using the same Microsoft account as before. It'll still say 'buy' in the store, but when you click on the 'buy' button, you'll get a message saying you've bought this before and do you want to reinstall.
You won't get billed again. I've downloaded a few paid apps I've bought on WP7 and I've not been refilled for downloading on my new WP8 phone.