Weight is a force, F=mg ie mass x gravity acceleration (expressed in simplest way)
When plane dives straight down (points to Earth's center) forces which are accelerating plane are weight and thrust. Opposing force is drag.
Now do the math.
Weight is relative to the acceleration of gravity. Mass is not. It's an absolute measure, function of an object density and volume. Weight and mass are not the same thing, though they are often confounded as such. For proof, take the weightlessness astronaut experience in orbit. They do not feel their weight. Their mass is not canceled. An object in free fall is weightless, not mass less.
When plane dives straight down (points to Earth's center) forces which are accelerating plane are
gravity and thrust. Opposing force is drag
and inertia(not really a force, rather a tendency to not change state IE : resisting acceleration/deceleration/change in direction). The acceleration granted by gravity is constant. If it's not true then Galileo, sir Isaac Newton and Albert Einstein (and might I add all physicist in between them and up to now) were wrong. I trust they were right. That's science. I know it's against common sense but it's true. Again, and I want it to be very clear, a given plane might dive better than another but it's not because gravity grants it more "thrust". Other factor are the cause. Airframe drag along with total thrust available at any given time determine how fast the plane accelerate through the dive. Gravity is a constant factor regardless of the mass of the plane.
Also I'd like you to define what make a good diver. A nimble zeke which control locks up at 400mph is not regarded as a great diver. A corsair which you can control at past 550 is a good diver. Even then both could accelerate quite well in a dive, one could maintain it longer before it begin shedding parts. I bet the zeke could even get faster. That is once it lost it's wings on the way down. Much less drag without those.
Take 2 good diver. Corsair and P-47. Who wins the race is dependent on how fast their engine can tow them through the dive and the drag generated by their airframe. Gravity is not a factor here because it grants them
the exact same bonus to acceleration regardless of their mass. And regardless of the steepness of the dive. The effect on an incline is also the same. Regardless of mass. This one was proved 4 centuries ago by Galileo.