Upgrading Headway consists of four steps:
If you’re upgrading from Headway 1.0 to 1.5 or newer, install and activate the Headway Widget Upgrader plugin. If you do not do this prior to upgrading, your widgets will be wiped out.

We at Headway firmly believe that WordPress’ build-in uploader is the easiest way to upload themes and plugins. If you know what FTP is and want to use it, you can skip this.
Once you have Headway on your desktop, go to the Add New Themes page under the Appearance module in the WordPress admin.

Once you’ve gone to the Add New Themes page, you will be greeted with a screen similar to the one below. Simply browse to your Headway zip file that you downloaded and uploaded. NOTE: You may be prompted for your FTP information. If you do not know what this is, ask your web host.

After uploading, you will see a page resembling the one below.

If you have used the custom.css file for CSS changes or used the custom folder for any reason, you are going to need to somehow transfer the custom.css and custom folder from your previous Headway folder to the new one.
We find the following steps to be the easiest:
After uploading, click Activate under Headway and presto!