Yep, it's all in the Ideal Rocket Equation:
Since you're holding the rocket type itself constant, the actual total thrust is constant. The final vertical velocity will therefore be roughly proportional with the mass differential between warheads so the rocket's range will also be affected by the increase or reduction in payload mass. The exact effect on the max range will also be affected by any additional engineering done to accommodate the change in warheads that increases or decreases the total mass of the payload complex.