Alternative option: Only weight votes cast in review - We could make it so the privilege is only awarded for reviewing and would only weight votes cast in close/reopen reviews.
Please don't do this. Some people close many, many more questions outside of review than in review. That should not deem their votes less valuable. Additionally, review queues on some sites are almost always empty (like here on MSE or on child-meta sites).
As an example, here are my current stats:
- On Stack Overflow, I've submitted 3,110 close votes vs 102 reviews1 in the "Close votes" review queue.
- On Meta Stack Overflow, I've submitted 140 close votes, only 8 of which are from review.
1 Only 80 of them are close votes.