Giving a confidence level is different from using weasel words. Weasel words make statements weaker or even vacuous. Confidence levels make statements more precise. Here's an example:
statement: Alice stole the briefcase
+weasel_wording: I think it's possible Alice could have stolen the briefcase
+confidence_level: I'd bet 5:1 that Alice stole the briefcase
Also note that I didn't say I wanted Dan to write less confidently. I wanted him to convey more varied confidence.
If there is any doubt regarding the stealing, then in this example i prefer the weasel wording version. The first one is incorrect, the last one you're suggesting an accuracy that you can't really back up, in order to convince someone.
So in this case the weasel wording doesn't make the statement weaker as it shows strength to admit you may be wrong.
