As Ron Garret describes, Time Machine is inefficient at backing up mailboxes in Apple Mail that have lots of messages and frequently change (even if it’s only one message that changed). This commonly affects the Inbox, Sent mailbox, trash, and SpamSieve’s Spam mailbox. To work around this problem, you can keep your “active” mailboxes small. Some ways to do this are:

• Periodically delete your old messages.
• Create “archive” mailboxes in Mail and periodically move your older messages into them. This allows Time Machine to create a single hard link for the entire mailbox.
• Setup Mail to automatically delete old spam messages. You can change the “SpamSieve” rule in Mail’s preferences to move messages into the trash, and then set Mail to automatically delete old messages in the trash. Or, you can set it up to put the spam into the Junk mailbox and have it auto-delete the old messages in that mailbox.
• Archive your old mail in EagleFiler. To do this, select the messages in Mail and press EagleFiler’s capture hotkey. After it’s finished importing, delete the messages from Mail and empty the trash. Once the mail is in EagleFiler, Time Machine will only have to back up one file for the whole mailbox. Since the file never changes (EagleFiler stores metadata such as tags and notes separately), Time Machine will never have to re-copy that data.