How to delete Gmail messages on your iDevices instead of archive
Go to m.google.com/sync (please note that the Google Sync features are only available only if you've setup your Gmail account as a exchange account). You might probably get an error screen of "unsupported device". Here is the trick: go below and find an option to change the language. Change the language to English (US). The screen will automatically refresh and you will have Google Sync screen.
Login using your Gmail username. You'll get into Google Sync configuration. Here you should see a list of your iOS devices that are configured to use Gmail.
*//Tap on the relevant iOS device.
*//You should now see an option to Enable "Delete Email as Trash", tap to select this option.
*//Tap on the save button.
That's it, now when you tap on the Delete button in the Mail app on that iOS device or you swipe to delete, Gmail should send the email to the Trash folder instead of archiving it.
Note:
Google Sync features are available only via Microsoft Exchange. Google Sync via Microsoft Exchange includes push email feature, which means that the emails will be delivered to your iOS device as soon as it arrives, unlike the regular Gmail account, which retrieves emails at x time basis.