There are some points in your code might need to review practically.

Here is something you might be interested to update and a method for you to var_dump the process.

function validate_attribute_weight( $passed, $product_id, $quantity, $variation_id = null, $variations = null ) {

    // Get custom field

    // 1. I am not sure if you directly get the post meta using WP builtin return expected result or not since I can see you use $product->get_meta() before
    // $weight = get_post_meta( $variation_id, 'custom_field', true );
    // $stock_weight_checkbox = get_post_meta( get_the_id(),'_stock_weight_checkbox', true );

    // you may try to change to
    // current product from the filter, it is better than get_the_id() because if filter provides to you, more directly and bullet-proof
    $product           = wc_get_product( $product_id );

    // with $product fetched, you may use the same code previously which ensure consistency 
    $stock_weight_checkbox = $product->get_meta( '_stock_weight_checkbox', true );

    if ( 'yes' == $stock_weight_checkbox && ! empty( $weight ) ) {
        // Get product object
        // $product = wc_get_product( $product_id ); // since already get, no need to do so

        // Get current product stock
        $product_stock = $product->get_stock_quantity();

        // ( Weight * quantity ) > product stock
        if( ( ( $weight * $quantity ) > $product_stock ) ) {
            wc_add_notice( sprintf( 'Sorry, you cannot add <strong>' . $weight .'</strong> of <strong>%1$s</strong> to the cart because there are only <strong>%2$sg</strong> left in our inventory. Please choose a lesser amount. We hope to have more in stock shortly.', $product->get_name(), $product_stock ), 'error' );
            $passed = false;
        }
    }

    // what you concern is the testing logic, if you want to intercept, you may add exit()
    // var_dump() here
    exit();

    return $passed;
}
add_filter( 'woocommerce_add_to_cart_validation', 'validate_attribute_weight', 10, 5 );

Because the WordPress ajax process is like:

• you click the add to cart
• it pass the data by JS ajax with URL and then return with something, it will fire the action to the php to process <== this is the point that you can intercept, when the php exit here, anything during the process is in the middle and thus you could see the var_dump();
• after process completed, the php return result (false/true) and return something to the page