Corporate jet Captain reported an NMAC with a balloon at FL430.

Narrative

We were in cruise flight at FL430 approximately 30 to 50 miles west of UIN traveling from ZZZ1 to ZZZ. Winds at altitude were approximately 300 at 65 knots. Our wind barb on our in Flight display showed a 46 not Tailwind. We were in VMC condition. As we were flying along at about 500 feet above us and slightly right of the nose; I saw a silver object. I pointed it out to the other pilot. It seemed stationary. As we passed under it; it looked like a cylindrical style of balloon. It was silver and appeared to have a tether similar in color hanging from the bottom. We reported to air traffic control and about five minutes later they made an announcement over the frequency to advise all aircraft in the vicinity of the object. After the fact; myself and the other pilot; weren't sure if this was a helium party balloon or something more scientific. With the winds; we discussed how it was odd that the string/tether didn't flow in the wind; almost as though it was a heavier material and more rigid than a string. My very first thought was that it was a my Mylar helium balloon in the shape of the number one. After a little bit of research the chances of a balloon of that type being more than 8 miles high seemed unlikely. There wasn't a whole lot of time to analyze what the object could be. Confusion set in for a moment initially as I tried to determine what it could be. Once I brought the other pilot into the mix we only had a couple of seconds before it passed over and behind us.