Hi clemyrd,
There are several steps that can be taken to help isolate the issues you've noticed. First, if you have multiple account set up on your Mac, check to see if this issue occurs with one specific account. If so, then check your email account using a web browser to see if you notice that mail continuously downloads. Then, send a message from your email account to see if it sends multiple copies when using a web browser. If you notice the same behavior, the best step would be to reach out to your email service provider for more help.
The following resource has some additional information that may be helpful: Troubleshoot email problems in Mail on Mac.
If you need more help, reply with the answers to these questions:
- If you connect your Mac to a different network, do you notice the same behavior?
- Does this happen with multiple email accounts?
Regards.