change size of point label in pgfplots [duplicate]

Question

I would like to change the font size of labels next to points in pgfplots.

As an answer to my previous question I got the following MWE:

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}

\begin{document}

\begin{tikzpicture}
 \begin{axis}[
  axis x line=bottom,
  axis y line=left,
  xmin=0, xmax=2.5,
  ymin=0, ymax=2.5,
  xtick=\empty,
  ytick=\empty,
  xlabel=position $x$,
  ylabel=time $t$,
  ]

  \addplot [only marks,mark=*,nodes near coords={\labelz},
            visualization depends on={value \thisrowno{2}\as\labelz}] 
  table[header=false] {
   0.5 1 a
   1.5 1 f
   0.5 2 g
   1.5 2 z
  };

 \end{axis}
\end{tikzpicture}
\end{document}

This works as expected and gives the following result:

In my real document, the label texts are much longer and don't properly fit in the graph. Now I would like to use a smaller font size for the labels. How can I achieve that?

----- EDIT -----

The solution suggested in the comment by LaRiFaRi (add the option every node near coord/.append style={font=\tiny} to axis) works, but the result doesn't look very pretty. Here are two screenshots of my graph:

Normal font size:

Tiny font size:

I think the problem is that I use math mode in the label texts.