You're adding a second pair of columns with the trailing &, which LaTeX reserves space for. Remove it.

I changed \text{a} and the similar constructs into a, because the traditional method for typesetting variables is using italic type. If you really want upright type it should be \mathrm{a}.

\documentclass{article}

\usepackage{amsmath}

\begin{document}

% this is just to show the center
\hspace*{\fill}\smash{\vrule depth 4cm height 0cm width 0.1pt}\hspace*{\fill}


\begin{align*}
a &= \frac{x}{y} \sim 1.5\times10^{-3} , \\
b &= \frac{y}{z} \sim 1.5\times10^{-1} , \\
c &= \frac{z}{a} \sim 1.5\times10^{-1} .
\end{align*}

\end{document}

In the code, the mysterious line is just to draw a rule in the center of the type box.

Note also the position of &, so that the different widths of the left-hand sides are compensated and the equals signs are aligned.

You're adding a second pair of columns with the trailing &, which LaTeX reserves space for. Remove it.

I changed \text{a} and the similar constructs into a, because the traditional method for typesetting variables is using italic type. If you really want upright type it should be \mathrm{a}.

\documentclass{article}

\usepackage{amsmath}

\begin{document}

% this is just to show the center
\noindent\hspace*{\fill}\smash{\vrule depth 4cm height 0cm width 0.1pt}\hspace*{\fill}


\begin{align*}
a &= \frac{x}{y} \sim 1.5\times10^{-3} , \\
b &= \frac{y}{z} \sim 1.5\times10^{-1} , \\
c &= \frac{z}{a} \sim 1.5\times10^{-1} .
\end{align*}

\end{document}

In the code, the mysterious line is just to draw a rule in the center of the type box.

Note also the position of &, so that the different widths of the left-hand sides are compensated and the equals signs are aligned.