I recently achieved a flag weight of 500 over on StackOverflow. I am curious as to why that has not resulted in my earning the Deputy badge. I realize that the description of the badge states that you must "achieve a flag weight of 500 by reviewing and flagging appropriately", but a fair number of my flags have not come directly through the review interface. I tend to spend most of my time browsing the site for questions I can answer, and flagging questions and answers that I happen across that I think should be flagged. Is this my problem? Do I need to have spent my time actually in the review interface?
Just wait a while. Some badges are awarded immediately, but others are not - an automated process generates them every so often.
So be patient, shouldn't take more than a day (in my experience).
From How do "badges" work?:
In some cases badges gained or lost may not show up immediately, but will instead be awarded the next time the system recalculates badges, which occurs periodically.