Why does a rocket engine that produces a constant thrust over a set period of time have less energy if it has more mass? (Zero-$g$) A rocket engine with the thrust of 1N working for 10 seconds will add more kinetic energy to the rocket if it is attached to a 10kg rocket and less if it is attached to a 20kg rocket. The rocket should consume the same amount of fuel if producing the same thrust for the same time with the same engine and so convert the same energy. So why doesnt it have the same energy. (I know the formula but why)
 A: Because you are ignoring the exhaust.  Also, I think you are only looking at this in the frame where the rocket starts at rest.  Let's look at that frame first.
When we have a force between two masses (like a bullet and a rifle) then:

*

*The change in momentum between both masses are equal

*The change in KE is greater in the object with lower mass.

If a suspended rifle fired a bullet, both would be given the same momentum, but the bullet would get far more of the energy from the work done by the expanding gases.
In the case of the rocket the same is true.  The greater the disparity between the exhaust mass and the rocket mass, the greater the proportion of the energy given to the exhaust (and the less the energy given to the rocket).  In the ground frame, the exhaust from the heavier rocket will have more energy (because it is moving faster).
(When you look at it from a frame where the rocket is already moving, this relationship isn't as simple because the rocket already has some KE that can be moved around).
A: Even if you assume that the change of the mass of the rocket, due to fuel consumption is negligible, the answer is that the heavier the rocket the smaller the variation of the kinetic energy. Details follow.

