You can buy replacement weights online!
I share a general search link below, but search replacement weight for bottom of lamp.
Oddly i went to 2 lighting stores & hardware stores and was told there isn’t any way and trash a perfectly good working floor lamp. A year later i still had it in storage & the idea popped in my head to check if there are replacement weights cuz this must happen a lot ( our lamp weight cracked & crumbled just like yours).
I realize you probably have remedied by now but I share this about searching online because someone else may with same problem may find this page topic just as I did.
https://www.google.com/gasearch?q=reolacement%20weight%20for%20floor%20lps&source=sh/x/gs/m2/5