Unfortunately, there is nothing you can do. If you agreed to allow 7 days per move, your opponent can take 7 days for each move. I got a winning advantage in one recent game in June, but my opponent didn't resign for another 5 months.
If you were a subscriber, this would merely be a nuisance. In your case, you have very few options: you could send a message with your next turn asking him to hurry up; you could accept that one of your six game slots is blocked for the next month or two or you could take out a subscription.