If the mailbox size is different in ESM and in Outlook

If you check a user's mailbox size in Exchange system manager and it shows a different value as compared to the mails you have in the outlook client then this might be one of the possible issues that the server is facing.

Go to --> HKEY_LOCAL_MACHINE\System\CurrentControlSet\Services\MSExchangeIS\<servername>\Private-<MailboxStoreGUID>

Check for the registry keys if present Background cleanup and Track Duplicates

Registry entry name: Background Cleanup
Value type: REG_ DWORD
Value data: 60000 (decimal) or 0xEA60 (hexadecimal) 4.

Registry entry name: Track Duplicates
Value type: REG_ DWORD
Value data: 1

If not present please create these 2 reg keys and after restarting the information store service the ESM mailbox size and Outlook mailbox size should be the same.