I would stay away from a weighted bottom... that, in my mind would make a big base that would still not really be very strong. I would go with anchoring both top and bottom... top to a stud and bottom either to a stud or concrete if you are on a slab.
I am sure many have done this before and some googling would help but what immediately comes to mind is something like a pipe flange on both ends to something secure... but those would need to be painted and/or polished to be made to look like anything other than a pipe going from the floor to the ceiling.
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