You can use the every mark
style; however, due to the way this style is processed, you need to add it to every axis plot post
to make sure all the keys are evaluated appropriately:
\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{
every axis plot/.append style={line width=0.8pt},
every axis plot post/.append style={
every mark/.append style={line width=1.6pt,draw=green,fill=red}
}
}
\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot coordinates {(-2,0) (-1,1) (0,0) (1,1) (2,0)};
\end{axis}
\end{tikzpicture}
\end{document}
The result:

Simply saying
\pgfplotsset{
every axis plot/.append style={line width=0.8pt},
every mark/.append style={line width=1.6pt,draw=green,fill=red}
}
in the above example won't have the desired effect.
An example using mark=x
:
\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{
every axis plot/.append style={line width=0.8pt},
every axis plot post/.append style={
mark=x,
every mark/.append style={line width=1.6pt,draw=red,scale=2}
}
}
\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot coordinates {(-2,0) (-1,1) (0,0) (1,1) (2,0)};
\end{axis}
\end{tikzpicture}
\end{document}

every mark/.append style
key detailed on Pg. 163 of the pgfplots v1.12 manual? If so, and it didn't work, can you please post a MWE and let us know what went wrong? Thanks!