If you download your website-based emails to Outlook on your computer there's a good chance that the message will stay on the server. This means that your allocated webspace will fill up and you will go over quota. This will result in bounced emails, potential lost business for you so it pays to do a bit of housekeeping and manage your emails effectively.
There is a setting on Outlook (2010 and 2013) that allows you to remove the email message on the server, either immediately after download or after a specified time. Using this feature will mean your allocation on the server will never exceed it's limit and you will have all emails already downloaded to your PC.
Your website allocation is limited as part of our terms of service. If you require an increase in allocation it means you will be using more of our resources - extra space on our servers cost £10 plus VAT per annum for every extra 500Mb of data you require. This could get expensive depending on how you manage your emails but there are more cost effective options available on request which we would be happy to help you with.
To set Outlook up to remove messages from the server after downloading and conserve space please follow this tutorial.