Beamer : Changing font size in notes when using \setbeameroption{show notes on second screen}

You can define font size for notes with \setbeamerfont{note page}{size=\tiny}, default size is \small.

Define the font size for notes as well as for subitems in notes with

\setbeamerfont{note page}{size=\tiny}
\addtobeamertemplate{note page}{\setbeamerfont{itemize/enumerate subbody}{size=\tiny}}{}

as shown in this answer.