How to change line spacing in an environment
If you look at the source code of setspace package, it can be seen that line spacing can be changed by modifying \baselinestretch. However, if you attempt to modify \baselinestretch in the following way, it won't work.
\begin{minipage}{\linewidth}
\renewcommand{\baselinestretch}{0.8}
Some think that love, strong, true, and self-sacrificing, is not to
be found in the Orient; but the story of Charan, which comes down
four hundred years and more, proves the contrary, for it still has
the fresh, sweet flavour of a romance of yesterday; albeit the setting
of the East provides an odd and interesting background.
\end{minipage}
Why? The answer is that you are missing a \par command at the end of the environment. That is, the following example will have line spacing correctly modified. This is the the same for \linespread command as well: one needs to terminate the paragraph with \par for the modification to take effect.
\begin{minipage}{\linewidth}
\renewcommand{\baselinestretch}{0.8}
Some think that love, strong, true, and self-sacrificing, is not to
be found in the Orient; but the story of Charan, which comes down
four hundred years and more, proves the contrary, for it still has
the fresh, sweet flavour of a romance of yesterday; albeit the setting
of the East provides an odd and interesting background.
\par
\end{minipage}
Therefore, you can rewrite the environment as follows. You can change 0.8 to your desired value.
\newenvironment{blurb}{\footnotesize\renewcommand{\baselinestretch}{0.8}}{\par\bigskip}
Setting line spacing programmatically
In the following example, I defined blurb* environment, which takes a font size command as argument. The line spacing will be automatically determined by a user-defined mathematical expression.
\documentclass[11pt]{memoir}
\usepackage{expl3}
\usepackage{xparse}
\chapterstyle{tandh}
\begin{document}
\makeatletter
\ExplSyntaxOn
% get base fontsize
\fp_new:N \l_base_fontsize_fp
\fp_set:Nn \l_base_fontsize_fp {\f@size}
\fp_new:N \l_now_fontsize_fp
\fp_new:N \l_new_baselinestretch_fp
% the command to compute new \baselinestretch based on
% base fontsize and current fontsize
\cs_new:Npn __compute_baselinestretch {
% set it to the sqrt of ratio between two fontsizes
\fp_set:Nn \l_new_baselinestretch_fp { sqrt(\l_now_fontsize_fp / \l_base_fontsize_fp) }
}
\DeclareDocumentEnvironment{blurb*}{m}{
\group_begin:
#1
% get current fontsize
\fp_set:Nn \l_now_fontsize_fp {\f@size}
% compute new \baselinestretch
__compute_baselinestretch
% use new \baselinestretch
\exp_args:NNx \renewcommand \baselinestretch {\fp_use:N \l_new_baselinestretch_fp}
\selectfont
}{
\par\group_end:\bigskip
}
\ExplSyntaxOff
\makeatother
\chapter{Charan}
\begin{blurb*}{\tiny}
Some think that love, strong, true, and self-sacrificing, is not to
be found in the Orient; but the story of Charan, which comes down
four hundred years and more, proves the contrary, for it still has
the fresh, sweet flavour of a romance of yesterday; albeit the setting
of the East provides an odd and interesting background.
\meaning\baselinestretch
\end{blurb*}
\begin{blurb*}{\footnotesize}
Some think that love, strong, true, and self-sacrificing, is not to
be found in the Orient; but the story of Charan, which comes down
four hundred years and more, proves the contrary, for it still has
the fresh, sweet flavour of a romance of yesterday; albeit the setting
of the East provides an odd and interesting background.
\meaning\baselinestretch
\end{blurb*}
\begin{blurb*}{\normalsize}
Some think that love, strong, true, and self-sacrificing, is not to
be found in the Orient; but the story of Charan, which comes down
four hundred years and more, proves the contrary, for it still has
the fresh, sweet flavour of a romance of yesterday; albeit the setting
of the East provides an odd and interesting background.
\meaning\baselinestretch
\end{blurb*}
\begin{blurb*}{\large}
Some think that love, strong, true, and self-sacrificing, is not to
be found in the Orient; but the story of Charan, which comes down
four hundred years and more, proves the contrary, for it still has
the fresh, sweet flavour of a romance of yesterday; albeit the setting
of the East provides an odd and interesting background.
\meaning\baselinestretch
\end{blurb*}
\end{document}

Reference
\par\bigskipat the end of the env to make sure the paragraph is ended while footnotesize is still active. – daleif Jul 20 '20 at 12:33