Lightweight HTML viewer

You have not mentioned a platform explicitly in the question, but from the context it appears like you are looking for a macOS app.

For the scenario you described, I'd advise you to use the Quick Look feature built into macOS. It lets you quickly preview a file's content in Finder. The default installation of macOS include support for common file types such as HTML (along with a host of other common file types such as PNG, JPG, MP3, PDF etc.)

To Quick Look your HTML file, simply click to select your file in a Finder window and press the Spacebar key. To dismiss the Quick Look preview, press the Spacebar key again or press the Esc key.

Quick Looking a HTML file will render the HTML preview of file instead of showing the HTML source.