Why does my arrow head size decrease?

Nodes are difficult beasts, and they offen reset scaling commands, but you can add a low-level scaling with \pgftransformscale{5}:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,shapes,positioning}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[]
\coordinate (b) at (-2,-2) ;
\node[circle,draw,postaction={decorate,decoration={markings,
    mark=at position 0.5 with {\pgftransformscale{5}\arrow[]{>}}}}] at (0,0) (u)
    {an arrowed circle};

\draw [postaction={decorate,decoration={markings,
    mark=at position 0.5 with {\arrow[scale=5]{>}}}}] (b) -- (u);

\draw [postaction={decorate,decoration={markings,
    mark=at position 0.5 with {\arrow[scale=5]{>}}}}] (b) circle (3);
\end{tikzpicture}
\end{document}

For all its limitations, things are a bit simpler in plain Metapost. There's no concept of a node, just points, paths and labels.

prologues := 3;
outputtemplate := "%j%c.eps";

beginfig(1);
% define the paths
path bar, c[];
c0 = fullcircle scaled 90 rotated 180;
c1 = c0 shifted 60 left;
c2 = c0 shifted 60 right;
bar = point 0 of c2 -- point 4 of c1;

% draw the arrows
ahlength := 8;
drawarrow c1;
drawarrow c2;
numeric t; t = 0.66;
drawarrow subpath(0,t) of bar; draw subpath(t,1) of bar;

% add the label
defaultfont := "texnansi-lmr10";
label("an arrowed circle", center c1);

endfig;
end.

If you wanted curved Computer Modern arrow heads, you could get them with the cmarrows package.