I would :

1. Check if there's a weekend between $start and $end :

   if($start_date->format('W') != $end_date->format('W'))

2. Then substract 48 hours for each week of difference.

   $difweeks = intval($start_date->format('W') - $end_date->format('W'));

   $duration = $duration - intval(48 * $difweeks);

I would :

$duration = $start_date->difference($end_date, 'hours');
// Place this :
if($start_date->format('Y-W') != $end_date->format('Y-W')) {
  $difweeks = $start_date->difference($end_date, 'weeks');
  $duration = $duration - intval(48 * $difweeks);
}
$entity_field[0]['value'] = $duration;

I would :

1. Check if there's a weekend between $start and $end :

   if($start_date->format('W') != $end_date->format('W'))

2. Then substract 48 hours for each week of difference.

   $difweeks = $start_date->format('W') != $end_date->format('W')

   $duration = $duration - intval(48 * $difweeks);

I would :

1. Check if there's a weekend between $start and $end :

   if($start_date->format('W') != $end_date->format('W'))

2. Then substract 48 hours for each week of difference.

   $difweeks = intval($start_date->format('W') - $end_date->format('W'));

   $duration = $duration - intval(48 * $difweeks);