By default, Outlook 2013/2016 behaves differently regarding the linked images. While previous versions of Outlook embed those into the message, Outlook 2013/2016 keeps them linked.
A registry change is required to make sure that Outlook 2013/2016 behaves similar to previous versions:
For Outlook 2013:
Key: HKEY_CURRENT_USER\Software\Microsoft\Office\15.0\Outlook\Options\Mail
Value type: REG_DWORD
Value name; Send Pictures With Document
Value: 1
For Outlook 2016:
Key: HKEY_CURRENT_USER\Software\Microsoft\Office\16.0\Outlook\Options\Mail
Value type: REG_DWORD
Value name; Send Pictures With Document
Value: 1
See Inline images may display as a Red X in Outlook for more information.