<?php if( date('U') - get_the_time('U', $post->ID) < 24*60*60 ) : ?>
<div class="bubble"><?php _e('NEW', 'mytheme_name'); ?></div>
<?php endif; ?>
the above one will show NEW div for each post posted in 24 hours. You can simply add anywhere in your posts loop.
You can use 7 * 24 * 60 * 60 to make it weekly. More info about php time is here.