I have a slow internet connection so I can't play video directly, I need to pause and wait for few minutes to buffer. I keep buffering in small player mode after buffering a while I make it full screen mode to watch. Now the problem is when I make it full screen some videos are starting to buffer second time from the point where I made it full screen and few of them are not.
Why?
Some videos on YouTube are uploaded in a high resolution, for example 720p (720 pixels vertical resolution). However, the player window itself is just around 380 pixels high.
When you watch the video in the small player, it doesn't make sense to buffer the high-quality version. You wouldn't see all the pixels anyway.
When you switch to full-screen, notice that the resolution indicator in the bottom right can change, for example, to 480p or 720p, which is a completely different stream. Therefore, it has to be re-buffered.
You can change this behavior under Settings » Playback Setup » Video Playback Quality:
The default resolution for small player mode is 360p, while switching to fullscreen will switch to 480p. In order to counter this, click on the resolution symbol and choose a resolution of your desire:
The lower the resolution, the faster it loads. Also once you modify the resolution, this video will stay in that resolution (and keep/continue preloading) even after switching to fullscreen or back.
