How to get larger item symbols for some lists in a Beamer presentation?

itemize symbols have font size hardcoded in definition (look at beamerthemedefault.sty or beamerbaseauxtemplates.sty).

% Itemize items, circle

\defbeamertemplate{itemize item}{circle}{\small\raise0.5pt\hbox{\textbullet}}
\defbeamertemplate{itemize subitem}{circle}{\footnotesize\raise0.5pt\hbox{\textbullet}}
\defbeamertemplate{itemize subsubitem}{circle}{\footnotesize\raise0.5pt\hbox{\textbullet}}

Section 16.3 "Changing the Templates Used for Different Elements of a Presentation" form beamer manual explain how to change it. It seems that would be possible to define a template with an option for font size. I don't know how to do it but a fast solution could be redeclare itemize symbols with new hardcoded size, something like

\documentclass{beamer}

\begin{document}    
\begin{frame}[t]{Frame title}
  \begin{itemize}
  \item First item
  \item Second item
  \end{itemize}
\bigskip
{\setbeamertemplate{itemize item}{\small\raise1.25pt\hbox{\donotcoloroutermaths$\blaktriangleright$}}
  \begin{itemize}
  \item Second first item
  \item Second second item
  \end{itemize}
}
\bigskip
  \begin{itemize}
  \item Third first item
  \item Third second item
  \end{itemize}
\end{frame}
\end{document}

EDIT: Changing balls for Madrid Theme.

Madrid Theme (beamerthemeMadrid.sty) uses \useinnertheme[shadow]{rounded} which declares \setbeamertemplate{items}[ball]. So we need to look for ball in beamerbaseauxtemplates.sty. To do it short, in this file some 'spheres' are defined and used. You can make your own definition,

\documentclass{beamer}
\usetheme{Madrid}

\makeatletter
\pgfdeclareradialshading[bg,parent.bg]{mysphere}{\pgfpoint{0.15cm}{0.15cm}}%
{color(0cm)=(bg!15);
 color(0.15cm)=(bg!75);
 color(0.3cm)=(bg!70!black);
 color(0.301cm)=(parent.bg)}

\defbeamertemplate{itemize item}{myball}%
{\raise-0.2cm\beamer@usesphere{item projected}{mysphere}}
\makeatother

\begin{document}    
\begin{frame}[t]{Frame title}
  \begin{itemize}
   \item First item
   \begin{itemize}
     \item first subitem
     \item second subitem
   \end{itemize}
   \item Second item
  \end{itemize}
  \bigskip
{\setbeamertemplate{itemize item}[myball]
  \begin{itemize}
   \item Third first item
   \item Third second item
   \end{itemize}
}
\end{frame}
\end{document}

The result is

I think sphere sizes are related with font size because they are declared using ex units but I'm not able to change its size with just a fontsize declaration. May be somebody else can help us.

Unfortunately the @Ignasi solution for change of the ball size is lacking in aliasing so the spheres have rough edges as you can see in the screenshot. To solve the problem, I modified the original definition in beamerbaseauxtemplates.sty by adding to preamble the following code:

% * original ball definition in beamerbaseauxtemplates.sty
%\pgfdeclareradialshading[bg,parent.bg]{bigsphere}{\pgfpoint{-0.1849315ex} {.2260273ex}}%
%{%
%  color(0cm)=(bg!15);
%  color(0.1643835ex)=(bg!75);
%  color(0.3287671ex)=(bg!70!black);
%  color(0.4520547ex)=(bg!50!black);
%  color(0.53ex)=(parent.bg)}

% modified by 1.4x multiplication factor
\pgfdeclareradialshading[bg,parent.bg]{bigsphere}{\pgfpoint{-0.2589041ex}{0.3164382ex}}%
{%
color(0cm)=(bg!15);
color(0.2301369ex)=(bg!75);
color(0.4602739ex)=(bg!70!black);
color(0.6328766ex)=(bg!50!black);
color(0.742ex)=(parent.bg)}  

\defbeamertemplate{itemize item}{myball}{\raise0.2pt\beamer@usesphere{item projected}{bigsphere}}

\setbeamertemplate{itemize item}[myball]

Now all item bullet balls are 1.4 times bigger then in default template and they have smooth edges.