Nitpicking, but ESP8266WebServer doesn't seem all that lightweight. Stuff like iterating through all headers to see if the searched one exists and if it exists, iterate again to get its value (::authenticate) or building new Strings from existing Strings (::_prepareHeader) aren't good signs.
The impact is probably negligible though (either because it's not were the CPU spends time or because the compiler is able to optimise most of it).
referring to the current master: https://github.com/esp8266/Arduino/blob/master/libraries/ESP8266WebServer/src/ESP8266WebServer-impl.h
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