Lightweight web app server for PHP?

have you taken a look at lighthttpd?

Back when Lighty was having many reports of memory leaks, someone mentioned Nginx. Ignore the ridiculous name, it's actually the best HTTPd I've ever used (and I've been using Apache since 1.1). Install PHP as FCGI rather than a module and you're golden.

You should try sng.

It is script which launches a PHP/Nginx development server quickly without any admin privileges. In is made in nodejs

You can install it very easily with :

npm install sng