Du måste lägga till enkel text $hobby bredvid varje kryssruta.
Korrigerad kod:
$query = "SELECT * FROM hobbies";
$result = mysqli_query($con, "$query");
while ($r=mysqli_fetch_array($result)) {
$hobby=$r["hobby_name"];
?>
<input type='checkbox' name='check[]' value='<?php echo $hobby;?>'> <?php echo $hobby;?>
<?php
}