android webview goes more than full width for responsive sites

You are missing a couple of setup calls that make WebView to render more like a mobile browser:

myWebView.getSettings().setUseWideViewPort(true);
myWebView.getSettings().setLoadWithOverviewMode(true);

Optionally, you can also enable pinch-zooming:

myWebView.getSettings().setSupportZoom(true);
myWebView.getSettings().setBuiltInZoomControls(true);
myWebView.getSettings().setDisplayZoomControls(false);

And as @Hylianpuffball correctly noted, your website should be ideally using <viewport> tag for controlling its presentation.