Jean, I highly appreciate your intricate reply.
I will start by saying that indeed my ability to explain this problem is limited by an incomplete formal education on the subject of mechanical engineering, to which I soon hope to satisfy time permitting. In the meantime this question I've introduced to you is a simplified example of a real-life issue I am trying to find a solution for. That being said and after reading your response, I will attempt to clarify my original post.
I read about "reaction force", though I am having a hard time relating that term to my "weight" question. I would appreciate if you could help me relate it better; I'm interested in learning about it!
I've attached another image. This time hopefully less confusing. At the far right side is an imaginary scale and I am interested in predicting what it will measure given the following criteria. The lever itself weighs 12 lb and is 204" in length. Your formula seems to indicate that the lever's center of gravity is at 204", though it's actually at 102". Does changing the last factor in your formula to R * (102"-26.5") make it so that solving for R will accurately predict what will appear on the scale?
Also, note the length of the green weighted object. Though I don't mention it in my drawing, does its distributed weight affect this prediction? I've only included its center of gravity as I assume that is enough. Am I wrong in this assumption?
Again, your help has been incredible and I egarly await your response!