The weights aren't needed to make it reproducable. The code and training data are needed. Hopefully if you used those, you'd ultimately reach the same result.
There is a whole other world between "released code" and "getting the results as seen in the paper".
Unfortunately. The reproducibility crisis is very much well and alive! :'( Much more to go into but it is a deep rabbit hole, indeedy. :'((((
IMO, having the weights available sometimes just papers over a deeper issue.
This boils down to framework implementations, timing issues and extra cost of trying to ensure determinism (without guarantees).