I'm currently leading a team to deliver an enterprise SharePoint online project covering data migration from SP2010.
The business are very keen to baseline current % of emails which are generated internally which include attachements so that we can measure (the hopeful) change in working practices where users are sending links once migrated to SP Online.
I've checked all of the standard O365 reports, spoken to most of the vendors in the O365 reporting market and explored the reports available via the REST reporting web service... but I've not been able to find a standard report which shows total number of new emails which contain attachements.
I am assuming that: - the emails are msg files that have been uploaded to your SharePoint 2010 environment as regular files - the email metadata such as To, From, Subject, hasattachments, ... is not available as SharePoint metadata.
Note: if the email metadata is available as SharePoint columns you may want to try using search or other reporting ways e.g. PowerShell.
BTW: using the size of an email is a poor indicator if an email contains an attachment. Especially if the emails uses html formatting.
The information whether an email contains attachments is stored in the property PidTagHasAttachments (http://download.microsoft.com/download/5/D/D/5DD33FDF-91F5-496D-9884-0A0B0EE698BB/[MS-OXPROPS].pdf). The only way to determine the % emails with attachments is to open each msg file, parse the binary msg file and then extract the value for the above property. This is not trivial (I have been there and ended up building an HTML5 solution). I am not aware of any tools / reports that provide this level of reporting for the contents of msg files.
How much data are you talking about? 10's of GB's or 100's of GB's or TB's? and what percentage of the documents are emails? Reason for asking: my company has developed a browser-based migration tool which extracts email metadata from msg files. It extracts fields like To, From, subject and also extracts the attachment details. See recording on https://youtu.be/KbGPLIzQ-lY (skip first 3 mins with general info). Using this tool to migrate the data will provide the number of emails with attachments. You can use it to migrate chunks to get "samples" of the % of emails with attachments or if the volume is not too high migrate everything to a test environment and then extract the numbers.