We can use the bullet analogy. Kinetic energy depends on velocity&mass,light bullet with high muzzle speed decays much faster than heavy bullet with low muzzle speed in air
Kinetic energy depends on m and v, here is the formula:
E kin = 1/2*m*v²
So a lighter warhead means faster velocity, more kinetic energy proportional to the V square.
Thus a higher Vmax always translates in more range than a higher m, if you throw 1 kg and 2 kg with same energy, the 1kg will fly faster and farther than 2 kg.
The work to get 2kg to the same distance as 1kg is therefore higher = larger rocket booster, more powerful propellant, yada yada.
The effect you describe is due to winds manipulating a light projectile's trajectory, but this is more of a fire arm catridge thing (under 1000 gram) than a ballistic missile warhead (~100kg or more kg) problem.
Also by miniturizing the warhead, we get a smaller warhead = lower cross-sectional area = less drag, lower RCS.
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