Google could attempt a traffic correlation attack when someone visits YouTube, Google or Gmail. They run the first hop and the web service. In Tor, this would be like running the Guard and Exit Node.
For example, Wade looks at the YouTube homepage, watches a video, returns to the homepage and watches another video.
For each of these actions, Wade's IP address to the Google proxy stays the same. Also for each of these actions, the YouTube account or cookie stays the same.
All of Wade's browsing uses the Google proxy, and YouTube can't see the IP address. But thousands of times, the same volume of data goes through the proxy at the same time YouTube sends it. Over time, Google could guess that IP address A is connected to YouTube account B.
For example, Wade looks at the YouTube homepage, watches a video, returns to the homepage and watches another video.
For each of these actions, Wade's IP address to the Google proxy stays the same. Also for each of these actions, the YouTube account or cookie stays the same.
All of Wade's browsing uses the Google proxy, and YouTube can't see the IP address. But thousands of times, the same volume of data goes through the proxy at the same time YouTube sends it. Over time, Google could guess that IP address A is connected to YouTube account B.