If all else fails check for a commented <body> tag before your <body> tag within the source code. Right-click the page and select View Page Source to eliminate this cause.
<!-- <body><script id="__bs_script__">//<![CDATA[ document.write("<script async src='/browser-sync/browser-sync-client.js?v=2.26.3'><\/script>".replace("HOST", location.hostname)); //]]></script> --> <body>
Browsersync appends its Java script after the first <body> tag it finds regardless of whether it is embedded in a comment or not! Obviously, being wrapped in a comment effectively disables it from injecting or refreshing the page.