The arrow head disappears because your are using the option axis lines*=middle. Instead of this, you could do axis lines=middle,enlargelimits=true as in my example below.
The lines are already thick in your example. If the comments below your code do not help, you will have to show us a compilable MWE of your situation.
% arara: pdflatex \documentclass{article} \usepackage{pgfplots} \pgfplotsset{compat=1.13} \begin{document} \begin{tikzpicture}[scale=0.8] \begin{axis}[% ,axis line style = thick ,domain=0:1 ,samples=50 ,axis lines=middle ,enlargelimits=true ,xtick={0,1},ytick=\empty ,yticklabels={} ] \addplot[color = black] {2/pi*asin(sqrt(x))}; \end{axis} \end{tikzpicture} \end{document}

axis line style=ultra thickoraxis line style={line width=2pt}.->:axis line style={line width=1pt,->}. You can select arrows style like in TikZ.