"My two cents". It's a phrase I use often, usually in debates where I find that both sides are so far off the mark that they have missed the main topic or purpose entirely. And so I resort to phrases such as "I think you've lost sight of it all, but that's just my two cents on the matter." No one asked for my opinion, but I sure in the hell am going to point out that the debate is too far off track.
The phrase is not really akin to "a penny for your thoughts." It is more of an American and Australian phrase meaning that one gives an opinion in a conversation that is, often, not asked for or wanted. It is also a phrase that is interchanging with "put your worth in." An example of this would be "She always has to put her two cents worth in! Why can't she just keep quiet?" It can also be used in this manner: "Stay out of this - if we want your two cents we'll ask for it."
"Two cents" is unsolicited advice, but also an "investment" (miserly) in the conversation. If one is to add their two cents, they should do so in a way that is not overbearing... after all, you are not really invested in the subject, and have decided to join in the conversation just because you have an opinion on the subject - a few pennies to spare on nothing. A wise speaker will use their "two cents" to make a strong point, perhaps to steer the conversation back to a more civil state. An unwise or rude person will use their "two cents worth" of time to make snide comments about something, or to show off how intelligent they think they are, especially as it pertains to the subject at hand.
The best users of the "two cents worth" rule are those who can add a proverb or thought without detracting from any of the other conversationalists. They offer a tidbit of information that only enhances the communication. You can take it (the comment) or leave it. Practice makes perfect. No one enjoys a 'buttinski', at any rate (be it two cents or a full dollar!)
I hope you don't mind my etymology lesson for the day. It is just my two cents worth for Sunday Scribblings.