Attiny85 using Arduino IDE, pull-up resistor voltage is too low

You can select different internal references, i just checked my nano which is using the default value and i measured 0 aswell, sorry for that confusion. On another project i selected 2.56V reference and measured 2.56V on Aref that´s why i stated that earlier.

Have you tried my code ?
Try to explain a bit what your sketch is doing and which libraries you are using.