set the table width to a particular value and each column's width proportional to its actual length

Question

I have a table and I want to set the table width to a specific value, say 0.8\columnwidth. After the stretching, I want each column's width is proportional to its actual width in the original table. After searching the tex.stackexchange.com, I find the posts about using the tabularx or the tabulary package to stretch the table width, but none of them achieve what I desire.

The former achieves something like this: The new column width are all the same, not proportional to its actual width.

The result the tabulary package produces is like this:

There is no stretching effect in width.

The minimum working example is:

\documentclass[12pt]{article}
\usepackage{lipsum}
\usepackage{tabularx}
\usepackage{booktabs}
\usepackage{tabulary}

\begin{document}
\lipsum[1]
% the original table
\begin{table}[h]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
 first column     & second column  & third column                    \\
\hline
 short       & longer longer &  longest longest longest  \\
\hline
short  & longer longer & longest longest longest \\
\hline
\end{tabular}
\end{center}
\end{table}
%table after using tabularx package
\lipsum[2]
\begin{table}[h]
 \centering
  \begin{tabularx}{\columnwidth}{|X|X|X|}
  \hline
   first column     & second column  & third column                    \\
  \hline
 short       & longer longer &  longest longest longest  \\
\hline
short  & longer longer & longest longest longest \\
\hline
\end{tabularx}
\end{table}

 \lipsum[3]
  % table after using tabulary
 \begin{table}[h]
\begin{center}
\begin{tabulary}{\columnwidth}{|C|C|C|}
\hline
 first column     & second column  & third column                    \\
\hline
 short       & longer longer &  longest longest longest  \\
\hline
short  & longer longer & longest longest longest \\
\hline
\end{tabulary}
\end{center}
\end{table}
\end{document} 

Is there anything wrong with my way using these two packages? or is there any other way to achieve what I want? Thank you in advance!