Here's a PHP function that receives two date strings and returns an integer with how many weekend days, Saturday or Sunday, occur within that date range.
```
function count_weekend_days($start_date, $end_date) {
    $start = new DateTime($start_date);
    $end = new DateTime($end_date);
    $interval = DateInterval::createFromDateString('1 day');
    $period = new DatePeriod($start, $interval, $end);
    $count = 0;
    foreach ($period as $date) {
        if ($date->format('N') >= 6) {
            $count++;
        }
    }
    return $count;
}
```
Optimization:
- Uses the more efficient `DateTime::format()` method to get the day of the week (as a number) instead of using date() function.
- Uses the more efficient `DateInterval::createFromDateString()` method to create the interval object instead of using new `DateInterval()` with a string argument.
- Uses the `foreach` loop instead of the less efficient while loop.

Example usage:
```
echo count_weekend_days('2023-02-20', '2023-02-28'); // Output: 2
echo count_weekend_days('2023-03-01', '2023-03-13'); // Output: 4
```
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