The lighter the spacecraft, the faster the rocket can move it, and the faster it goes, the sooner it can get to Pluto.
Currently, the New Horizons spacecraft is traveling away from the Sun quite fast, about 9 miles (3 kilometers) per second. If it burned all the hydrazine in its tank, it would accelerate by only about 1/8 mile per second (1/5 km/s). So it could speed up or slow down (depending on the direction of its thrusters) by only a tiny fraction of its velocity.
Astronomy magazine subscribers can read the full answer for free. Just make sure you're registered with the website.