You can use a short one liner Command to get the mailbox size have added | more in the end of the command so that you can press enter to proceed with a big list
you can remove it if you wish to export it.
To Check for the local Server
Get-Mailboxdatabase | Get-MailboxStatistics | Sort TotalItemSize -descending | FT Displayname, TotalItemsize, Itemcount Database –Autosize | more
To Check for Database Level
Get-Mailbox –Database “Database Name” | Get-MailboxStatistics | Sort TotalItemSize -descending | FT Displayname, TotalItemsize, Itemcount,Database –Autosize | more
To Check for Server Level
Get-Mailbox –Server “Server Name” | Get-MailboxStatistics | Sort TotalItemSize -descending | FT Displayname, TotalItemsize, Itemcount,Database –Autosize | more
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Hope its Useful !!