PHP has lower overhead still. You don't need to import, explicitly define route, etc. PHP Built-in dev server doesn't require anything extra either.
I mean, it's "different", but I think it's a stretch to say lower. PHP overhead is suddenly a lot higher when you need a route with a dynamic ID in it if you're talking pure out-of-the-box, for example, which is a reasonably trivial use case.
I contest the idea that sinatra-style frameworks are "huge".
Python + flask is about as low-overhead as one can get. No need to set up any extra (apache || nginx).
PHP's model of "just chug along returning null" by disabling most relevant errors is a massive antipattern in production code.