They are vibration dampers and their purpose is to reduce vibrations at the ends of the handlebars. Do they do any good? It depends on who you ask. In my case I took them off when I put Kuryakan grips on. Didn't feel any difference but figured that that the Honda engineers know what they are doing. I purchased a set of chrome dampers and put them on. After 56,000 miles I can honestly say that my hands have never tingled after a long days ride. Those handle bar grips are a long moment arm from their attach points and that will allow any vibrations to be amplified at the ends. The next post will probably disagree with me but you have my opinion.
First there is a bit of road related vibration that gets transfered to the bars. And the engine is mounted directly to the frame without the aid of rubber so engine pulse and toque also will be transfered to the frame and handle bars. This is the kind of vibration I feel through the bars and the weights are perhaps ment to dampen this affect. And if the bike tips all the way over it protects the clutch and brake levers. You see this on sportbikes a lot also.