How can I increase the size of the beamer navigation symbols?

The template you are looking for is called navigation symbols and is defined in beamerouterthemedefault.sty through defbeamertemplate*{navigation symbols}{default}. One approach is to create alternative symbols through a redefinition of insertslidenavigationsymbol & Co. but something way simpler is to use an adjustbox for the whole thing and redefine it. An example to scale it to 80% of the paperwidth:

documentclass{beamer}

usepackage{adjustbox}

defbeamertemplate*{navigation symbols}{enlarged}
{%
    adjustbox{min width=0.8paperwidth}{%
        hbox{%
            hbox{insertslidenavigationsymbol}
            hbox{insertframenavigationsymbol}
            hbox{insertsubsectionnavigationsymbol}
            hbox{insertsectionnavigationsymbol}
            hbox{insertdocnavigationsymbol}
            hbox{insertbackfindforwardnavigationsymbol}%
        }%
    }
}

begin{document}
frame{TEST}
end{document}

In case visual impairment is an issue, you could also redefine the color of the elements to be more prominent, e.g. in black and a dark gray (black!60) by stating:

setbeamercolor{navigation symbols}{fg=black!60}
setbeamercolor{navigation symbols dimmed}{fg=black}

The result: