I would verify that their Exchange account is the only account within outlook. From a few different places it looks like it could be something stuck in Drafts too (although you said you checked there). Possibly removing the account and re-adding it in Outlook could be the quick fix to it (although they would lose their saved autocompletion which a lot of people complain when they lose it).

Im running 2016 on probably 25 Mac's and haven't seen this issue yet, but I have had weird issues with Outlook in general that aren't worth the time messing with and just adding the account back again will fix saving all of our times.

Outlook 365 Attachment Size Limit

Outlook For Mac 2016 Attachment Size Limit Size

How to Increase Outlook Attachment File Size, Microsoft attachment file size limit #increaselimit #outlookattachment #emailattachment. Limit the size of your attachments - This is a general guideline; for slower, connections (such as a mobile device) you should use a much smaller size, such as 250 kilobytes (KB). If you must send larger attachments, verify the maximum size of the message that you can send.