You need something like this:
$args = array(
'post_type' => 'post'
);
$q = new WP_Query($args);
if ($q->have_posts()) {
$date="";
while ($q->have_posts()) {
$q->the_post();
$m = get_post_meta($post->ID,'field_id',true);
// var_dump($m);
if ($date != $m) {
// if $m is a strtotime compatible string
echo date('l',strtotime($m));
$date = $m;
}
echo '<br>';
the_title();
echo '<br>';
echo str_repeat('-',200);
echo '<br>';
}
}
A lot depends on the format of your “date/time info” in the custom meta field though, and you do not specify. I am also not sure if that meta_key is unique per post. I assumed it was.