When adding Custom Blocks the weight is changed for the rest of the blocks
If you have blocks that have the same weight, that may trigger a bug where your blocks get shifted. At least, this is something I have experienced with views filters in D7, and I found a bug report here regarding a similar weight issue in D8 with taxonomy terms: https://www.drupal.org/node/941266

Ensure you are able to see the numerical weights of the blocks, and make sure they all have distinct weights.