Create a backlight group and add the pi user to it:
sudo groupadd backlight
sudo usermod -a -G backlight pi
Create a udev rules file:
sudo nano /etc/udev/rules.d/99-backlight.rules
...with the following contents:
ACTION=="add", SUBSYSTEM=="backlight", RUN+="/bin/chgrp backlight /sys/class/backlight/%k/brightness"
ACTION=="add", SUBSYSTEM=="backlight", RUN+="/bin/chmod g+w /sys/class/backlight/%k/brightness"