Auto-fill with select Woocommerce checkout

Question

I have the following code to generate a select and bring values within options:

add_action( 'woocommerce_after_order_notes', 'cliente_woocommerce' ); 
function cliente_woocommerce( $checkout ) 
{ 
global $wpdb;

$results = $wpdb->get_results( "SELECT * FROM tab_clientes" );
$options  = array( '' => __('Selecione o cliente') );

// Loop through the data query results
foreach($results as $result) {
    $options[$result->nome] = $result->razao_social;

}

echo '<div id="cliente_woocommerce"><h2>' . __('Cliente') . '</h2>';

woocommerce_form_field( 'cliente', array( 
    'type' => 'select', 
    'class' => array('cliente form-row-wide'), 
    'label' => __('Campo de Teste (Cliente)'), 
    'options'   =>  $options,
), $checkout->get_value( 'cliente' ) );

woocommerce_form_field( 'nome', array( 
    'type' => 'text', 
    'class' => array('nome form-row-wide'), 
    'label' => __('Razão Social'), 
    'default'   =>  '',

), $checkout->get_value( 'nome' ) );
woocommerce_form_field( 'cnpj', array( 
    'type' => 'text', 
    'class' => array('cnpj form-row-wide'), 
    'label' => __('CNPJ'), 
    'default'   =>  '',


), $checkout->get_value( 'cnpj' ) );


echo '</div>';

with the following script:

       <script>
        $(document).ready(function()
        {
            $('#cliente').change(function() {
                $('#nome').val( $( this ).val() );
            });
            $('#nome').change(function() {
                $('#cnpj').val( $( this ).val() );
            });
        });
        </script>

When I select the client, the #name (social reason - in the table = social razao_social) field appears with the correct value, but the value repeats inside CNPJ.

What I’m doing wrong?