Things to test (you might already have tried some of these):
Do videos played from local storage (hard disk, memory stick, cd/dvd etc.) also freeze up or is it just videos from the web? If it does, the problem is likely to be something to do with your laptop, like video drivers.
To assess if it is a problem with a particular website try videos from a different website to see if they work. If they do, the problem is likely to be an issue with a particular website. (unlikely though since your computer freezes up but sometimes network timeout situations can lock up your computer)
If you have access to the internet in another location, try the same there. Do the videos from the same website still cause freezes? If it works ok, the issue could be related to your internet connection.
Ok, that was the "have-you-turned-it-off-and-back-on-again" checks. Now on to your system.
Video from the internet is most likely Flash video so browse to www.adobe.com
and look for the Flash Player in their downloads. Download ind install the latest version.
Go to Sony's website and look for drivers for your laptop. In particular, check for updated video drivers and network drivers and download and install both.
Try using a different browser. Some browsers have problems vith the Flash Player. At the time of writing this Google Chrome is particularly troublesome with jittery video. I don't know your level of expertise but the three most common browsers are chrome - http://chrome.google.com, firefox - http://www.mozilla.org/en-US/firefox/new/
and internet explorer - http://windows.microsoft.com/en-GB/internet-explorer/download-ie.
Try all three flavours of browser but also download and install Flash Player in each browser.
Hopefully something here should help fix your issue. Please reply and let us know if any of this worked or if you tried it all and it still does not work.