Reducing the distance the bow rises up, will lessen its fall.
So in cabin weight should go forward even if it lightens the stern. The stern never has a pitching problem.
(I apologize that this was written for an earlier discussion on this topic in which a similar point about where weight should be placed to minimize pitch.)
I am afraid that is not how it works, at least not in a wave train. Putting weight towards the ends of a boat does nothing good for a boat. To explain, boats pitch around an instantaneous pitch axis (which is called 'instantaneous' because the actual longitudinal and vertical position changes as the boat's pitch angle changes).
And for any given pitch angle there is a moment of inertia, which is the derived from all of the weights on a boat, and their distances from the instantaneous pitch axis. Whether you move a weight 10 feet forward of the pitch axis or 10 feet up from the pitch axis, or 10 feet aft of the pitch axis, or ten feet down from the pitch axis for that matter, it has the same effect on the pitching moment of inertia. No matter where in the boat that weight is located, the further it is located from the pitch axis, the greater the pitch moment of inertia. The more that the weight in question weighs, the greater the pitch moment of inertia.
When a boat with a larger pitch moment of inertia encounters a single short duration wave, (all other things being equal), it will move more slowly, but through a larger pitch angle than a boat with a smaller pitch moment of inertia, because the boat with the larger pitch moment of inertia stores more kinetic energy (momentum) and that kinetic energy carries it past the point that the wave is still lifting it or dropping it.
In a wave train, a boat with a smaller pitch moment of inertia (all weight concentrated near the pitch axis) will tend to more closely follow the rise and fall, and face angle of each wave. A boat with a larger pitch moment of inertia will tend to get further out of phase with the waves, and so have harder impacts with the waves and so encounter more force, which in turn causes it to want to pitch much more than the frequency and height of the wave would suggest.
So a boat with a larger pitch moment of inertia will tend to have a more comfortable motion in a single wave, but a much less comfortable motion in a wave train.
Of course countering the rotational forces, and motions, are dampening forces which derive from the shape of the hull.