Increase upload file size by content type
It sounds like the content type "story" has a 3MB limit set on that file field.

You can increase that limit by browsing to "example.com/admin/structure/types" and select the "Manage fields" tab (for the "story" content type). Find the field in question (the file upload field) and edit it. You should find a setting for the maximum upload size there.

If you'd like to learn more about fields, and specifically file fields, check out this Drupal.org resource and and this one as well.

Now, the other thing you will need to review is your .htaccess file. There are a couple of php flags you will want to review:

php_value post_max_size
php_value upload_max_filesize


Review the .htaccess file first because no matter what setting you set for your file field on the content type "story", it will be overridden by the setting in the .htaccess file.