Big heavy trailerables
One could write a book on this topic. Some responded to your question with their experiences of water ballasted boats. They are not considered to be heavy (assuming you want to sail off shore or have a boat that will hold up in more extreme conditions). The beauty of water ballasted boats are they are larger (but not heavier) vessels that can be trailered down the road with a smaller vehicle because they are light when empty and when launched, you add the ballast in the form of water. Many of the MacGregors, Hunters and Catalinas have offered such boats. I don't think Hunter has them anymore, however. For those sailing in protected waters, wanting this ease of trailerability they might be good choices. Some of these boats offered quite large interiors with enclosed heads, large aft berths and so could accommodate a growing family. The downside to these boats, in comparison to boats with other keel configurations is they can be tender. The reason being is that the ballast is contained high within the hull and not below the hull like a boat with a conventional keel. Also water is lighter than lead and so when you have your ballast within the hull and not below the hull, your "counterbalance" is not as effective. To compensate this the manufacture of a water ballasted boat often shortens the mast so that the combined center of effort of the two working sails is lower. That is a compromise to performance. A high aspect ratio mast with a higher combined center of effort and a keel properly positioned low enough to maintain stability is a much more fun boat to sail - generally speaking.
That being said, there are other alternatives if the above info is not what you want. Boat keel configurations that are considered to offer more stability would be the type such as a swing keel, shoal keel, winged keel or shoal keel with a centerboard, daggerboad drop keel or tandem keel, Sheel keel or end plate bulb keels. In some cases you will find some boats with some internal ballast as well as a swing keel (Chrysler 26 is one example).
Swing keels are usually made of cast iron because you cannot use lead for this purpose. Lead is heavier and offers more stability per volume (also more expensive). Swing keels can offer a great deal of stability to provide a sufficiently stiff boat, but consider that some swing keel boats are only self-righting if the keel is down and not all (but some) are if the keel is in the up position. Swing keels are also often not very hydrodynamicaly shaped which doesn't help performance. But, swing keels usually extend down in the water to help windward performance, but obviously not as efficient as fin keel that has a nice foil shape. Winged keels can be lead or cast iron, but usually not cast iron as the wings can be too vulnerable to bending if lead on smaller boats. The wing concept is to offer a shoal draft configuration that provides as much lift as you can expect in a shoal keel (borrowed from America Cup technology). The problem is, they aren't very efficient, especially to weather and if you run around or out of water in sand or a soft bottom, they act like anchors and you can have a bad time getting free. Sailing down wind or on a broad reach is ok with a winged keel, but to weather, not very good at all.
A shoal draft keel used on many O'days, Columbias, etc. years ago, were longer fore and aft, but not very deep. Again, because they are below the hull and made of lead (even if encapsulated within the fiberglass hull) offered good stability, but not good windward performance. Later, manufacturers started putting centerboards in these shoal keels which extended deep into the water and that provided decent windward performance. In my opinion, this is the best overall keel configuration for a trailerable boat with the least compromises to performance. To my knowledge, the only currently manufactured boat that offers this design is Precision.
I forgot to mention that many swing keel boats had trunks in the cabin that took up living space or was in the way, while a boat with a keel below the hull uses up no interior space.
Today, if you buy a new boat they are offered most of the time with either a standard deep keel or an optional shoal keel. The deep keel comes with the price of the boat, but you pay extra for the shoal keel. Why you say? Because since the shoal keel is not as deep, it is larger and hence more lead or material is used, which increases it's cost. But, this is not really so much a condition of a trailerable boat.
S-2 made many designs (rumored to again restart manufacturing) that were performance oriented that included daggerboard type lead keels. They were efficiently shaped for performance and did have sitting accommodations for 4, but they are sought after racing boats rather than cruising boats and there was this big thing in the middle of the boat to contain the keel. Another example of this design was the C&C Mega 30 (a Peter Barrett design) where the keel pulled up into the hull via an electric winch. (S-2 used a manual winch). This keel was a faired NASA fin with a bullet bulb on the bottom. Very efficient and performance oriented, but some purchased them for cruising as it was 30 feet and you could launch and retrieve it and step the mast yourself. Another example was the South Coast 26A which had a drop keel lifted and lowered by an electric winch, but the keel didn't have a NASA shape and had a huge bulb on the bottom. Both the Mega and Southcoast were legal width for trailering and both had stand up headroom. The SC had an enclosed head too. Incidentally, the South Coast 26 was the exact same hull used in the Parker Dawson center cockpit boat, but her keel was a swing keel.
Another keel configuration is the full shoal keel (of varying depths) with the attached or barn door rudder. Cape Dory and many more designs are examples, many of which are not necessarily considered to be trailerable boats.
The tandem keel used on many European models are twin keels with an attached bulb. Different designs have come out through the years and some more efficient that others. Bavaria uses the tandem keel on their modern shoal drafted boats and it is proving to be quite efficient and stable, but again, I have not seen these on trailerable boats.
Sheel keels and end plate bulb keels (different from each other) use a concept of a shoal keel with a flare out at the bottom to add some lift and stability. The end plate concept (a Jim Taylor design) is pretty efficient in a shoal draft keel used on trailerable boats.
There is a compromise to everything it seems, so you, as a buyer and sailor really have to figure out what your priorities are and what is important to you in a boat. Where will you sail and how long do you intend to stay on board? I presume the trips would be weekend trips or trips that are a few weeks long. But, not months or over great distances or offshore.
Boats geared for offshore use are built to those specifications and classified as offshore capable. Most trailerables are not considered more than inland or coastal capable. Catalinas, Beneteaus, Hunters, MacGregors, Precisions, O'Days, etc. are not classified for offshore sailing.
In addition, when you think of taking very long trips you have water tanks, fuel tanks and storage capacities to take you away on a long trip. Even when looking at large sailboats, you can be romanced by the appeal of a particular design, and interior space, but if her inboard auxiliary cruising range is limited by a small diesel fuel tank, she might not be the boat for that purpose, etc.
I remember the late Lyle Hess designed some sturdy trailerable boats that could be sailed off shore.
But, I assume that you are not going to go sailing off into the sunset in your trailerable boat.
Larger trailerable boats would include: Clipper 30 (old design - not too many around and not really super well built. But, it was 30', about 8' wide and trailerable). C&C Mega 30 mentioned before. Hake 32, built still today (and they have a number of smaller ones too). Shannon has a large, quality trailerable boat. Beneteau built a shoal draft, twin rudder boat that could be put on a trailer, but it was not legal width (need permit) and cannot step mast by yourself. Not in production now. Hunter, of course made many, of which the 260 was probably the most popular (water ballasted). MacGregor made several and even made one that was 65 feet. But, not built for offshore, most had sitting headroom and some were designed to have large outboards (the X series). Precisions built cabin boats from 16.5' to 23', but have built larger sizes in years past. South Coast and Parker Dawson, Spirit Yachts (Glastron company), Bayliner Buccaneer (used concrete for ballast - not built anymore, large interiors, sailed terribly and not rugged). American built well built boats that were very trailerable up to 26', but were boxy, had a shoal keel with no centerboard. Lancer had similar designs. O'Day made many through the years and at one time might have been the most popular sailboat manufacturer of her day. Aquarius and Balboa and Laguna. Spindrift, Cape Dory, Cal, Columbia, Coronado, San Juan, WD Schock, Morgan yachts, Irwin Yachts, Paceship, There are lots more I can't think of now. I will think this over and maybe offer some insight to big heavy trailerables (which sort of defeats the purpose of trailerability)