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Does this happen even though you don't tap any field where you can input text? The keyboard should only pop-up when you tap a field where you can type something. Tapping somewhere else on the page will hide the keyboard.
If this happens on certain web pages the problem could perhaps be that a text field is auto selected by the web page.
Which browser are you using in the tablet? If using Chrome, try installing the latest version from Google Play.
Are you using the standard keyboard or a 3:rd party keyboard?
Is your tablet updated to Android 4.2?
Could you give me an example of a webpage where this happens?
There must be something wrong in your tablet. When i open www.google.com using Chrome my keyboard doesn't pop-up. Only when i tap the search box or address field i can see the keyboard.
Try clearing data for Xperia keyboard under Settings -> Apps -> All and see if that helps. If not i recommend that you try making a repair of the software using PC Companion.