I am a little short of time but let me see if I can give a quick explanation. First lets start with a simple example. If you visualize a hull that was essentially a simple cone in shape balasted so that the point was at the surface of the water, you could spin it all day long and it would not change trim in a manner that would tend to force the pointy end down.
While the design process for a hull is obviously more complex, what allows a wider stern boat to heel with out going bow down, is that the hull is modeled so that the longitudinal center of buoyancy does not shift as the hull is heeled (at least through moderate heel anglee). Designers have simply shifted the longitudinal center of buoyancy aft but, of course, the longitudinal center of gravity has also moved aft in the hull the same amount as the longitudinal center of buoyancy. As a result the boat can heel without changing fore and aft trim at least through through small angles of heel (perhaps as much as 20-30 degrees of heel).
This of course requires careful modeling to maintain the same longitudinal center of buoyancy as the boat heels. Computer modeling becomes really critical to this process but most good modeling tools will show the center of buoyancy at various heel angles allowing the designer to move a little more buoyancy aft or forward to maintain trim with heel.
Although a very crude design compared to more modern designs, the pictures of my boat under sail demonstrates how little change in trim can occur with heel angle even on a boat with an extremely broad transom and fine bow. You can find a number of useful pictures on the Cruisers Forum Website:
The best picture to understand this is the one labled "Synergy Bearing away". Here she is heeled roughly 30 degrees and you can easily visualize that while any individual segment of the forward portion of the hull builds increased buoyancy slower than the transom area, the bows proportionately larger area and longer lever arm offsets the comparatively rapid increase in volume in any individual segment near the transom.
The following was exerpted from an earlier discussion of this topic:
"There seems to be a lot of discussion about why newer boats have wider sterns. There are a lot of reasons that modern boats tend to have wider sterns but increased accomodations is not necessarily one of them. More on that later. If we look a little bit of history, after the Fastnet disaster a lot of attention was focused on what makes a good seaworthy boat. Motion at sea became a popular research topic. Hull forms and weight distribution was studied in great detail. One of the trends that came out of all of that study was boats with longer waterlines and finer bows. Moving the waterline forward reduced pitching and making the bow finer reduced the impact with waves in a chop.
"As bows became finer the center of bouyancy moved aft as well. At first this produced boats that developed a lot of weather helm as they heeled and which tended to jack their rudders out of the water and wipe out easily. As designers got better at modeling hull forms this became far less of a problem.
"This combination of fine bow and powerful stern sections were found to offer exceptional upwind performance and reaching speeds that are substantially higher than theoretical hull speeds. So this fine bow, more powerful stern hull forms were really a win-win design trend that offered greater speed, coupled with better motion comfort and seaworthiness.
"In a recent issue of Sailing World (More than a year ago now) there was an interesting couple paragraphs dealing with theoretical hull speed which touched on the issue of theoretical hull speed as it relates to these new hull forms. I am quoting here:
"Waterline''s affect on hull speed is theoretical and not absolute. As a hull goes faster, the bow wave stretches to the point where the bow and stern wave become on wave cycle, whose wavelength is equal to the waterline length. This brings us to wave theory. "
"The speed of a wave (in knots) is equal to the square root of the wavelength (in feet) multiplied by 1.34. If your boat has a waterline length of 32 feet, the theoretical hull speed is 7.6 knots. The waterline length is thought to limit the hull speed because if the boat goes any faster the stern waves has to move further back taking the trough between it and the bow wave along with it. As the trough moves aft, it causes the stern to drop, making the boat sail uphill."
"Except for planning designs, sailboats typically can''t generate enough power to go any faster and climb their own bow wave. But a boat with extra volume in the stern can exceed its theoretical hull speed because the extra bouyancy prevents the stern from dropping into the trough. By the same token, a fine-ended design might not achieve its theoretical hull speed if buoyancy in the stern is insufficient." (Written by Steve Killing and Doug Hunter).
I do think that it is a bit of a stretch to say that these broader sterns resulted from trying to stuff in additional accommodations. I say this because as the stern gets broader, displacement is removed from the bow thereby reducing usable accomodations volume in the bow. If anything the accomodations are just shifted aft a bit. That is not necesarily a bad thing as the stern is generally a quieter area with less motion than the bow."
I need to get back to work!