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Ps = (thrust - drag) * velocity / weight
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If you look at that relationship you can see that all else being equal (thrust, drag, velocity) increasing weight ALWAYS reduces Ps.
It always reduces Ps (in absolute value...), but not always the height of the zoom. Ps only tell you the rate of energy gain (per mass). It is not a direct measurement of the zoom. The benefit of the mass is implicit in this equation - it is in the time and the sign of Ps. Note that if Ps is negative, weight actually INCREASE Ps!
So, when is Ps negative? when the thrust is weaker than the drag. Most commonly this would be when the speed is high enough, so if the zoom is started from very high speed, the weight gives an advantage in the first part of the zoom - this is a ballistic-like phase (a stone thrown up into viscous air). Then as the speed drops, so does the drag and the thrust will eventually turn Ps positive - this is the climb phase, where engine pull significantly affects the dynamics and weight becomes a hindrance. Just remember that the drag dominates when the velocity is high, and we are multiplying by velocity to get Ps, so it becomes highly negative very fast. Thrust will dominate at low velocities, so if (thrust-drag) part increase, velocity typically decrease and Ps does not increase as much.
The time domain is a little more complicated. There is a third scale that affects the dynamics. Put in the term used in the Ps expression: "g" the gravity acceleration which competes with "thrust/mass" and "drag/mass". In WWII fighters, g is always the largest since the thrust is no where near as strong as gravity. This is why the differences between planes are not huge.
The biggest effect of some extra thrust/mass is how the zoom will look like close to its peak, rather then how high it will be (even though it will). The thrust, even if much weaker than gravity will make the last part of the zoom longer (in TIME) where the plane will appear to be "hanging on its prop". It is not really going anywhere (this is when the speed approaches 0), but it is not starting to fall either. Note that in the Ps expression, low velocity means small Ps and when it is close to zero it does not matter much how close it is. This is the phase where the plane gains the most from having low mass - but it is not much in terms of gaining alt because the velocity is low!
When the thrust starts to be a significant fraction of the weight, then things really start to change and mass makes a huge difference. Of course, for planes with thrust>weight, there is no proper "zoom" anymore - it is just a vertical climb.
