Add the Outlook Anywhere URL to the Local Intranet zone. See screen shot below. The URL to add here is
https://mail.webville.net While you're here, if you have SharePoint and you'd like to make that login easier, add your SharePoint URL here as well.
Click the Close button and Ok button to return to the security tab. While on the Security tab, select Local Intranet zone and click Custom level. The dialog shown below will appear. Scroll to the bottom and verify that your computer is set to allow Automatic logon in the Intranet zone. That's the default setting, you probably won't need to change it. See screen shot below.
Click Ok to close the Local Intranet Zone security settings dialog. Choose the Advanced tab of the main Internet Options dialog. Look near the bottom of the settings list under Security for Integrated Windows Authentication, it should be enabled. See screen shot below.