Setting line width when using set layers in pgfplots

Question

I've been using pgfplots for some plots. I prefer using relatively thick lines in my plots which I feel are better suited to the font I'm using in my figures, accomplished with something like line width=1pt in the options to \begin{axis}. However, I'm now in the process of adding a second y-axis to a plot. The pgfplots manual says that I should use set layers. However, when I add set layers, I lose the effect of changing the line width. Any ideas for how I can get the line width parameter to stick to the axis lines, ticks, plot line, and so on?

While hunting around, I stumbled upon Bug in TikZ? Line width on layers which seems related, but since I'm not really a TikZ or pgfplots expert, I'm not sure how to apply the conclusion in that Q&A.

Here's a simple example using a single axis and plot, which shows the problem I'd like to overcome:

\documentclass{minimal}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}


\begin{document}

\begin{tikzpicture}

\pgfplotsset{set layers} % commenting this line makes line width work

\begin{axis}[
    xmin=0,
    xmax=4,
    line width=1pt,
    every tick/.style={black}
]

\addplot {x^2};

\end{axis}
\end{tikzpicture}

\end{document}

With set layers active (undesirable behaviour):

After commenting set layers (what I want to see, but while using set layers):

Answer 1

see if this helps:

\documentclass[margin=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}


\begin{document}
\pgfplotsset{set layers=axis on top,
             axis line style={line width=1pt},
             every axis plot post/.append style={line width=1pt}
             }
    \begin{tikzpicture}
\begin{axis}[
    xmin=0, xmax=4,
            ]
\addplot {x^2};
\end{axis}
    \end{tikzpicture}
\end{document}