Flag weight is the total number of flags marked as
valid helpful minus the number of flags marked as invalid declined for a given user. That number is used…
… well, it's shown on a user's profile, and it's used for a couple of badges, …
… oh, and there's one useful thing: it's used to prioritize Stack Overflow's huge flag queue. But there are better ways to do that.
Now the case for the prosecution: flag weight gets discussed a lot. Most of this discussion isn't helping anyone, it's not making SE a better place and it's wasting moderators' time. Flag weight also gets people to flag for the sake of flag weight, at best wasting moderators' time and at worst harming the site. And recently there's been some friction with moderators — the recent flag dismissal reform.
So please remove the concept of flag weight altogether, as well as the distinction between
valid helpful and invalid declined flags. Keep the optional ability for moderators to give feedback — meaningful feedback, as opposed to the single bit of signal that existed until recently. Feedback could be things like “we don't do community wiki for that stuff any more” or “yup, the question is off-topic, but that migration makes no sense” or “you could have cast a close vote”.
(The “send feedback” button does just that. If the input text is empty, that button is a simple “dismiss”. Closing or deleting the post automatically dismisses without sending feedback, so if you want to send feedback, do it first. UI design is not my forte, so feel free to improve.)
Flag weight is supposed to “deter serial abusers”, but there's no need for such a complex tool, and it doesn't deter all abuses anyway. If a moderator sees a suspicious flag, we have the option to go through the user's flag history (please keep that!) and visually eyeball if that user had a lot of bad flags. Visually eyeballing is fine to detect serial abusers.
N.B. Although this post has been marked status-completed, my request has not been implemented. Flag weight and flag validity have not been removed. Flag weight is no longer displayed on profiles, which is an improvement, but flag validity still exists, leading to arguments about rejected flags, which are the only way to provide feedback, but are often perceived negatively.