I'm sure the limitation is 960*540 on screens with resolutions of 1920x1080. Smaller values may be related to the aspect ration of the video itself.
The limitation comes from the specification used for this feature and it's just a recommendation. But most browsers make use of it:
It is also RECOMMENDED that the Picture-in-Picture window has a maximum and minimum size. For example, it could be restricted to be between a quarter and a half of one dimension of the screen.
If you really need larger views than 50% of the current screen, you are able to make use of popup windows and play the video in there or use the Fullscreen API. A challenge with the popup method is that the windows won't have a always on top
-flag and/or option to activate it.
Another method would be to make the video element drag- and resizable. This would be similar to many instant messenger video players.