Go to your widget settings and click on "4. API Key" > "JavaScript" section of the page, there you should see JS code like this:
Copy the JS code snippet and go to your Weebly admin menu, then go to the Themes menu and click on Edit HTML/CSS button on the bottom left corner of the page.
Click on the header.html file and paste the code before the </body> tag like in the screenshot below.
Save it, then go to your website and if u did everything correctly, you should see the widget in the bottom right corner.