[Tex/LaTex] ‘LaTeX’ logo with kerning issue and not scaling properly

Question

I recently discovered that the \LaTeX command does not have proper kerning between the first ‘L’ and the ‘A’, the ‘A’ looks too thin (like fake smallcaps, simple downscaling). Also the logo doesn't scale properly when choosing the \tiny font size (the A gets out of proportion). I use the libertine package, so Linux Libertine. How to fix this?

\documentclass{article}
\usepackage{libertine}

\begin{document}
\centering
{\tiny\LaTeX}

\LaTeX

{\Huge\LaTeX}
\end{document}

Answer 1

With metalogo:

\documentclass{article}
\usepackage{libertine}

% keep the original for reference
\usepackage{letltxmacro,xpatch}
\LetLtxMacro\oldLaTeX\LaTeX
\LetLtxMacro\oldTeX\TeX
\xpatchcmd{\oldLaTeX}{\TeX}{\oldTeX}{}{\ddt}

\usepackage{metalogo}

\setLaTeXa{\scshape a}
\setlogokern{La}{-.3em}
\setlogokern{aT}{-.1em}
\setlogokern{Te}{-.08em}
\setlogokern{eX}{-.1em}
\setlogodrop{0.33ex}

\begin{document}

{\fontfamily{cmr}\selectfont\oldLaTeX}

\LaTeX

{\tiny\LaTeX}

\end{document}