Test date object against previous date in loop

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.