Limit size of emails

There's no way to avoid downloading attachments, but if some of these are not important to you then they can be removed permanently using a fairly new feature. The attachments are then removed both locally and on the server, that is, lost forever if you don't have a copy. In 1.9.6 you can right-click and attachment to find “Remove Attachment”. In the 2.0BETA there's also a “Remove” button and a “Message ▸ Remove Attachments” menu item which can be applied to multiple emails in one go.

If using this feature then it's useful to select “All Messages”, enable the “Size” column, and click on it for sorting by size. Then you can quickly see which emails take up the most space.

I hope this helps.