You can get low flag weight simply for difference of opinion. Case in point:
That's the answer the OP selected as THEIR answer. The comment, "-1 what does this have to do with anything," is inappropriate in my opinion especially seeing that the OP found it very relevant.
Furthermore, if we're supposed to flag noise, then comments like, "Why the hell are people upvoting this??" very much should be flagged by users as they add nothing to the conversation.
I've been watching the past couple days what posts or comments I flag and which ones get labeled as "invalid". Both of the above cases where labeled invalid. I would certainly love to hear the argument that it's actually an abuse to flag these comments.
I can't see the options that moderators get for discarding flags but it seems, based on the effect on my flag weight, that it's either/or with no in-between. Either something you flag is deleted and thus your flag is considered "valid", or it is not and your flag is "invalid". Is there really no, "Yeah, I kinda see your point but I'm not going to delete the post," kind of selection? If there is, are moderators simply choosing not to use it??
I've also noticed seemingly unbalanced application of these two options. When something gets lots of flags, it gets deleted, when it gets fewer it does not. The actual content of the flagged thing matters much less than the amount of people flagging it. Thus if you're not part of a mob sitting in a chat room picking people to flag (or "focusing the community" depending on what side you sit), legitimately or not, a completely legitimate flag may be tossed by a moderator. I am not a big fan of mob justice (it simply isn't) so in all honesty I find this rather tragic, especially since people are now actually penalized for doing what they think is right. Perhaps there is a reasonable argument that posts that bother more people should be deleted and those that don't bother the community as much, even if the content is exactly the same, should not...but if this argument is legitimate then penalizing those who just happen to be in the minority is not.
With these various things in mind, none of which should be at all surprising or can be helped, it seems like quite a heavy hand to actually doc people for flagging things they legitimately see as inappropriate. It's even a greater heavy hand that actually decides to suppress the flags from such people. That being said, I see two ways to resolve the problem that could still limit the impact of people who "habitually abuse the flagging system":
1) Implement the flag weight similarly to voting. 2) Make sure there's a third option that neither deducts nor increases the weight of those who flagged the post. The use of "inappropriate flag" would then be for more obviously abusive flagging.
Personally I don't think the first is as good as the second because it's still possible to have legitimate gripes about things that moderators simply don't see as inappropriate either for some users or as a whole.
Furthermore, I don't think it's enough just to label a flag as "invalid". Should there not be a reason for such an act? As I was perusing the mod tools today I saw a couple that I really would have deemed actually invalid since the flagging reasons where absurd, it would be easy to express that. If a participant in SO is going to be penalized for something in such a way that can impact their ability to flag abuse I think it's quite unfair that nobody even bothers to tell them why. Simple dismissal of a flag may not require so much effort but if a user is being penalized I do think it's the right thing to do.
Penalizing people without telling them why has never been effective and has not, as far as I can tell, been accepted as legitimate in any but the most extreme dictatorships.
Of course, I've got a very low weight so nobody is inclined to listen to me anyway. Hopefully though as I show above the reasons for my flags are, in my opinion, completely legitimate.
Also, I certainly hope it is the case that flags are basically anonymous. Human nature is human nature and moderators are human beings. Human beings develop biases. This should not be allowed to affect their application of this system. The SO developers are bright people so I'm sure a flag is just a flag in the moderator view.