How do I make the LM3914 (LED) Bar-graph driver IC make the LEDs light up brighter?
From the datasheet:


  The current drawn out of the reference voltage pin (pin 7) determines LED current. Approximately 10 times this current will be drawn through each lighted LED ...


Since the voltage is 1.25V, the current in the schematic will be:

\$ {12.5\text{V} \over {1\text{k}\Omega+3.9\text{k}\Omega}} \approx 2.55mA\$

Reduce the resistances in the divider to about 1/8 of their current values.