Hi Hampo,
Im afriad having POP3 really doesnt help this situation as you are using a third party ISP to send the large emails. How far back do your emails go? Hvae to tried exporting them to a .pst file as a backup and then deleting as many emails as you can to free up some space? If not then I can gladly go through the steps with you
Once you have deleted some of your inbox, junk, sent and deleted items after you backed them up and it still doesnt work, there are plenty of compression softwares that I can recommend that can make sending emails with large attachements simple yet affective!
Regards,
Brock_UK