On your Outlook configuration, there is a setting which says, "Leave read email on the server", something like that. You must access your GMail account in POP3 mode for this to work.
Check also GMail settings, in "POP and IMAP" tab.
Keep in mind if you do that, your email is now only on the local PST file. If the file gets deleted, corrupted, hard drive crashes, you delete emails by accident, there is no copy saved on the server for you.