1) You need to log in to your Webmail account and delete items to free up usage space (make sure you also delete items in the Deleted Items" folder too)
2) Alternatively you can set your Outlook to remove messages from your Webmail (by default it is set to do so) but if it's not you can go to Tools->Options->Mail Setup->Email Accounts-> click on the active email then click "change"->More Settings-> Advanced tab->Delivery field choose your preferred option
