I personally don't at all like the idea of "close vote weight" because it just makes the system too complicated and confuses users as to why the question was closed by fewer users than normal. If it's not a binding vote, then it should be a regular close vote.
Also, as you have demonstrated, it's quite easy to get a bronze tag badge before you even gain the privilege of voting to close questions. We don't want users who have never even participated in actual close votes before having increased weight in certain tags. It only takes 100 votes for a bronze tag badge, which means it can be achieved with as little as 1,000 reputation. A gold tag badge requires 1,000 votes in a single tag, which in a simple world implies the user has gained at least 10,000 reputation on the site overall. At that point the user has much more experience with the site and can be safely trusted with increased weight on their close votes (even if it only applies to duplicates at the moment).