The argument that best supports the student's claim is: "Heavier objects need greater force than lighter objects to accelerate at the same rate."
This statement aligns with Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma). If the same force is applied to two boxes and one accelerates more than the other, it implies that the box with greater acceleration (likely box 1, in this case) must have less mass than the other box (box 2).