This bug seems to be the cause of other threads that have been made on the issue of animation weight not replicating, such as
There is a workaround for developers who want to blend animations using Weight in their games, until this is resolved.
Upon further investigation I found out that there is one working way to replicate the weight of animations to other clients:
- Play animations with a weight of 1 (not 0)
- Ensure AdjustWeight never sets to 0 (0.01 at minimum)
The issue seems to be related to other clients stopping animations when Weight is set to 0. By using this workaround you can achieve your desirable effect until Roblox fixes this issue.