How can I increase the font sizes used by the WordPress visual and HTML post editors?

Put this on the top of your functions.php file after the first <?php

add_action( 'admin_print_styles-post.php', 'my_admin_css' );
add_action( 'admin_print_styles-post-new.php', 'my_admin_css' );
function my_admin_css() {
?>
<style type="text/css">
#editorcontainer textarea#content { font-size:130%!important }
</style>
<?php
}

The function will print out the additional CSS on the pages where you write posts only (so it’s not loading on every admin page), and applies a font size increase … adjust as required..
Source

The above code will work for HTML mode, for Visual mode, edit the editor-style.css, it’s included with the theme .. (it’s used to make the Visual editor render text the same as it’s shown on front side of your side of your site – you’re of course welcome to make changes to that file).
Source

I hope that helps.