The problem is with your email account settings. You have to check the box on your computer( no settings on your phone app for this?) to delete emails from the server or uncheck the box to leave messages on the server. Otherwise the emails stay on the pop server until the account hits its size limit and start deleting the oldest. Your problem is caused by the email pop server system thinking it hasn't sent some emails, or some other system failure, and re-sends them. It usually occurred multiple times with Verizon but I changed to Comcast and GMail and now I haven't had this happen for years.
Bingo. After a few weeks, the messages get cleared from the email app on the phone, and because they are still on the server, the server re-delivers the message because it thinks the client hasn't received it yet. The client should be smart enough to not download the same message twice...but apparently not.
Most folks don't want the server to delete their messages after downloading on phone *IF* they are also using POP on a desktop client, i.e. Outlook, or simply want to retain the message on the server.
This is why I HATE POP for email. In today's world where people want access to their mail in more than one place, it is a horrible way to manage mail access.
The OP didn't specify what kind of mail accounts these are, but do have access to other protocols perhaps, such as IMAP or Activesync? At the very least most email providers will have IMAP enabled...which works MUCH better than POP3.
If you haven't already tried it, can I also suggest K9 email app? It's free and pretty basic, but has a lot more available setup options for non-standard accounts than the builtin email app has.