Because Google Apps (Gmail) automatically puts a copy of your sent items in the Sent Items folder, it's rather redundant for Outlook to do this as well. Although Google Apps prevents the creation of doubles, it's better to just let Google Apps do it, as it's one less thing to upload (particularly useful on slow connections).

To turn off the copy of sent items in Outlook, turn off the option Save copies of messages in the Sent Items folder. You'll find this in the Outlook options in the Mail tab, section Save messages.