This a great exercise to develop single leg power and stability.
Emphasising the stamping on the box enables you to focus on driving through the glutes and hamstrings on the lead leg and eliminates much of the assistance from the trail leg. Try not to think of stepping onto the box and pushing up, but stamping down hard so the impact drives you up.
Finish with a quick pause at the top of the motion to brace through the abdominals and squeeze the glutes forward.
As we are focusing on speed of movement this does not require a huge amount of weight.