Pin 15 is the backlight LED anode and pin 16 is the cathode. The current required by the backlight can be higher than the pin can provide, a transistor should be used to switch the backlight on or off, for "Always On" a direct connection to a 5v line is needed.
Pin 3 is the contrast pin, it needs a voltage output of between 0 - 5 volts, the arduino can't output voltage levels. It has PWM support, but that needs an RC circuit to create a stable voltage.