Staging Lab.

Once the lower stage's propellant is spent, its tanks, engine and structure are just dead weight. Discarding that 25 t of empty hardware means every remaining unit of upper-stage propellant accelerates a lighter vehicle — but the discard itself is not an instantaneous velocity gain.

A vacuum-optimized upper-stage engine reaches a higher effective exhaust velocity than a shared, atmosphere-tolerant design. The same propellant mass ratio produces more delta-v at a higher exhaust velocity, per the rocket equation.

The two-stage vehicle starts 4 t heavier than the single-stage counterfactual, because of the extra engine and structure. Staging wins here despite that extra mass, not because it is free.

That is also why rockets don't keep adding stages indefinitely. Every extra stage carries its own engine and structure as dead weight for the rest of the flight, and that dry mass directly shrinks the delta-v the rocket equation gives back — on top of the added cost and complexity of building a new engine for it. Past two or three stages, the extra weight outweighs the gain, and the benefit shown in this tool reverses.