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.