Sort Popular Posts by Views for the Last Week

Use strtotime to compare dates.

$start = strtotime('yesterday');
$end = strtotime( '+1 week',$start);

$args = array(
    'posts_per_page' => 5,
    'ignore_sticky_posts' => 1,
    'meta_key' => 'sw_post_views_count',
    'orderby' => 'meta_value_num',
    'order' => 'DESC',
    'date_query' => array(
        'after' => $end,
        'before' => $start,
    ),
);

$popularpost = new WP_Query( $args );

if ( $popularpost->have_posts() ) {

    while ( $popularpost->have_posts() ) {
        $popularpost->the_post();

        // Do your stuffs

    }

} 

Please note, this will return the posts from last 7 days, not last week.