You should/could have mentioned that you use the original definition from
the sidenotes package and try to change the definition of one of the
commands using the functionality of the xparse package which is loaded automatically with the sidenotes package.
I replaced \@sidenotes@placemarginal{#2}{\textsuperscript{\thesidenote}{}~#3} with \@sidenotes@placemarginal{#2}{\textsuperscript{\thesidenote}{}~\footnotesize#3} (added \footnotesize before #3).
In addition, thanks to Christian Hupfer, you need to enclose the definition with \makeatletter...\makeatother since the code uses the @ symbol in the not literal way (see What do \makeatletter and \makeatother do?).
\documentclass{article}
\usepackage{sidenotes}
%% Loads the following packages
% marginnote
% caption
% xparse
% l3keys2e
% changepage
%%% From the sidenotes documentation
%% \sidenote
%% Uses \sidenotetext
%\NewDocumentCommand\sidenote { o o +m }
%{
%\sidenotemark[#1]
%\sidenotetext[#1][#2]{#3}
%\@sidenotes@multimarker
%}
%
%% \sidenotetext
%% Used in \sidenote
%\NewDocumentCommand \sidenotetext { o o +m }
%{
%\IfNoValueOrEmptyTF{#1}
%{
%\@sidenotes@placemarginal{#2}{\textsuperscript{\thesidenote}{}~#3}
%\refstepcounter{sidenote}
%}
%{\@sidenotes@placemarginal{#2}{\textsuperscript{#1}~#3}}
%}
% \sidenotetext
% Used in \sidenote
% Changed to meet the question of user J. Bratt (https://tex.stackexchange.com/questions/361622).
\makeatletter
\RenewDocumentCommand\sidenotetext{ o o +m }{%
\IfNoValueOrEmptyTF{#1}{%
\@sidenotes@placemarginal{#2}{\textsuperscript{\thesidenote}{}~\footnotesize#3}%
\refstepcounter{sidenote}%
}{%
\@sidenotes@placemarginal{#2}{\textsuperscript{#1}~#3}%
}%
}
\makeatother
\begin{document}
Hello\sidenote{Hi}
\end{document}
\IfNoValueOrEmptyTF? Ah, that's an invention bysidenotespackage. You're missing a\makeatletter...\makeatotherpair – Apr 01 '17 at 15:22\@sidenotes....macros expand somewhere else so\makeatletterisn't needed actually – Apr 01 '17 at 15:39\makeatletter...\makeatotherdoes not harm here anyway. – Apr 01 '17 at 15:42