My "weißensee" mailbox is very full. How can I archive important emails and free up space? (macOS X)

We can temporarily expand your mailbox. You can then remove the deleted emails by opening the trash and "permanently delete deleted files". However, in the short term you should also use the gained storage volume to archive older e-mails - especially those with large attachments.

To archive, create a folder in the Finder (with subfolders if needed). You simply drag and drop the eMails from the list in the eMail program into this folder and then delete them in the eMail program. The eMails archived locally in the folder on the computer remain searchable and can be opened simply by double-clicking in the eMail program.

By the way, the eMails are also much safer there than in the eMail program, where power failures, hacker attacks, hardware failures, etc can cause data loss in the worst case.