Bold Greek letters are not as bold as Roman letters

Question

This question was discussed here previously, but no answer is provided.

Greek letters are made bold using \boldsymbol, however they do not look bold at all compared to bold Roman letters, particularly they are within the text and if the text is also Roman.

Consider the following MWE:

\documentclass[]{article}
\usepackage{amsmath}
\usepackage{amssymb}
%\usepackage{upgreek}
\usepackage{newtxtext,newtxmath}
\usepackage[]{bm}

\begin{document}
\noindent
Bold Roman: $\textbf{M}$, $\textbf{a}$, $xyz$. These look OK.\\
Bold Greek: $\boldsymbol{\uppsi}xyz\boldsymbol{\psi}$. They do not look bold at all.
\end{document}

and the result is

Also consider the default font:

\documentclass[]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{upgreek}
%\usepackage{newtxtext,newtxmath}
\usepackage[]{bm}

\begin{document}
\noindent
Bold Roman: $\textbf{M}$, $\textbf{a}$, $xyz$. These look OK.\\
Bold Greek: $\boldsymbol{\uppsi}xyz\boldsymbol{\psi}$. These are a little bit better but still not bold.
\end{document}

and the result is

Edit:

Here is an example text to see the characters better. To me, Roman characters are immediately catching the eye as bold, but not the Greek letters:

Is there a way to have "real" bold Greek letters?

Edit (based on David's comments):

Use of \pmb with Roman text (second line):

Use of \pmb with default text (second line):

Edit:

I have added Troys suggestion below. I think this look gives immeadiate impression of a matrix.

Answer 1

A nice solution adapted from another question:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{newtxtext,newtxmath}
\usepackage{pdfrender}

\newcommand*{\boldgreek}[1]{%
  \textpdfrender{%
    TextRenderingMode=FillStroke,%
    LineWidth=.35pt,%
  }{#1}%
}
\begin{document}
  $\psi$
  $\boldgreek{\psi}$
  $\uppsi$
  $\boldgreek{\uppsi}$
\end{document}

You can modify the line width to your liking to make the letters more/less bold.