To start off all sustainence in the interface of the OS, it uses at least one transparent texture over the window of the browser on slower devices gives performance issues - first check how it works youtube after you enable the classic theme.
Put google chrome, it is not a panacea but in practice he has better hardware support out of the box... at least it will allow to understand whether to try to solve the problem on or all, no more options.
Full screen mode video playback slow? usually in this mode, the video output directly to the screen bypassing the extra layer of buffers and other slag.
p.s. on slower machines, youtube is usually seriously stress the CPU, i.e. a simple data load (pause), it's shocking but that's the reality edit it using the plugin, substituting the html5 player to something more bright (just remember linux set browser extension, which has launched the youtube videos in a separate mplayer window, it strongly helped), try to Google browser plugin mplayer youtube. However, there is a problem, these extensions may not already be supported.
Very good support for youtube and still heaps of streaming services supports command line utility youtube-dl, it is recommended to timely upgrade (ie what goes normally with ubuntu most likely won't work or will be absent from the struggle with the likes of Google), for example, using the pip (including windows), ie you can not only play video at the link but to save disk space (streams video/audio by default, it stitches them), learn a few tricks with ffmpeg and write a simple bash script/cmd to view the video you will only need a couple of taps on the keyboard (something like copy link to clipboard and press the combination of buttons that runs your script).