The possible problem
if your checkout button appears twice after a Woocommerce plugin update, one problem could be that your form-checkout.php file is not compatible with the latest version.
The fix
For example it could be located in your themes folder in a template override structure such as explained here
A template override location would look something like
yoursite/wp-content/themes/your-theme/woocommerce
form-checkout.php would then be located in:
<span style="color: #993300;">yoursite/wp-content/themes/your-theme/woocommerce/checkout/form-checkout.php
Make a backup of the file, and then insert the file from the woocommerce plugins folder, overwriding your file in the above mentioned location.
The file you need is located here:
yoursite/wp-content/plugins/woocommerce/templates/checkout/form-checkout.php