This is fairly simple to achieve, first rename the name attribute to my_categories[] this is then passed as an array.

Then you will need set the values of each checkbox as the category id. In this way you can loop though the array my_categories[] and then set the categories present in that array.

Here is a simplified example : // In your callback function for metabox, // This should be inside a loop. term_id">

<?php 
// This should be hooked to the save_post action of appropriate post type.
if(!empty($_POST['my_categories'])) { 
    foreach($_POST['my_categories'] as $cat) 
        { 
            echo $cat; 
            //echoes the value set in the HTML form for each checked checkbox.
            //In your case the ids of selected checkboxes, now all you need to do is set those categories.
        } 
    } 
 ?>

Now you have all the ids of selected categories in an array, which is easier to process. Use your logic to set the categories.

This is fairly simple to achieve, first rename the name attribute to my_categories[] this is then passed as an array.

Then you will need set the values of each checkbox as the category id. In this way you can loop though the array my_categories[] and then set the categories present in that array.

Here is a simplified example : 

// In your callback function for metabox,
// This should be inside a loop.
<input type="checkbox" name="my_categories[]" value="$term->term_id">


<?php 
// This should be hooked to the save_post action of appropriate post type.
if(!empty($_POST['my_categories'])) { 
    foreach($_POST['my_categories'] as $cat) 
        { 
            echo $cat; 
            //echoes the value set in the HTML form for each checked checkbox.
            //In your case the ids of selected checkboxes, now all you need to do is set those categories.
        } 
    } 
 ?>

Now you have all the ids of selected categories in an array, which is easier to process. Use your logic to set the categories.