Before offering to help, find out which part the other person wants to keep doing themselves.

Taking over can remove something a person was holding on to. In a hard stretch, the tasks someone still manages are often the last places they feel useful, and a well-meant offer to handle everything can quietly strip that away. What helps is the part they would be glad to be rid of, which is not always the part you would choose.

Ask before you act. Say you would like to take something on and ask which piece would be most welcome. Accept the answer even if it seems like the easy bit, and leave them the jobs they want to keep.