When I give someone some information, and say "for what it's worth", I mean that this information might be irrelevant to him (but probably not to me), or that I know that he might not accept what I am saying. It could also be something that is not worth very much in terms of information content, or be somewhat extraneous.
When I say, "as a matter of fact," I am giving information I know
Hmmm...no. Not really. Now, what I'm saying is only based on how I understand the expressions as an native speaker but I haven't actually studied English:
You would say "I agree with you, for what it's worth" or "In my opinion, for what it's worth" or "For what it's worth, I don't think you should meet him again". When saying "for what it's worth" you're recognizing that you are only giv
If you add for what it's worth to something that you say, you are suggesting that what you are saying or referring to may not be very valuable or helpful, especially because you do not want to appear arrogant.