When I tested it - I don't normally have a pic in my signature - I did not have this problem you described. Off hand I can think of a few things that may affect it that you could test out. It could be the type of file that makes a difference: jpg, gif, png, etc. It could be the file size - there could be a limit at which it becomes an attachment. It could be the settings of the receiver email client, perhaps if it is set to block images. Or it could be settings on the email server of either the sending or receiving email provider that make all pictures become attachments.
When I tested it I just sent an email from one exchange account to another exchange account and did not have it show up as an attachment and did not get a double picture in the signature either. So hopefully you can find a way that makes yours work. Another thing you can try to see if it makes a difference is instead of the insert picture method, you could try copying the logo to your clipboard and then pasting it in your sig. Maybe that will prevent whatever is causing it to be an attachment for you.