Balanced ship designs tended to have 8-9 guns for complex reasons linked to the interaction of armament weight vs armor weight to stop the same caliber of shells. A smaller number of guns makes it hard to fire rapid salvos, required to spot your fall of shot and thus shoot accurately against moving targets. Salvo spotting BTW works on the basis of the mean point of impact, the center of all the splashes. That tells you where your aim of all your turrets is actually landing, any one splash tells you very little. Before the 1943-44 period you had to do all of this by visual observation, from the spotting top or an aircraft. Even the earliest radar could provide accurate range, but not bearing, nor track your splashes prior to this. But no battleship laid down after 1942 was ever completed anyway.

A larger number of guns then 9 meanwhile tends to rapidly increase the ship size, which means much greater cost. People would rather build more battleships then mount more guns. You see more guns in earlier dreadnoughts, but those dreadnoughts tended to both be slow and have little deck armor because they did not expect to fight at long ranges. Increased speed and deck armor greatly increased ship sizes. The earlier ships could 'afford' the extra guns while still controlling size and cost growth. The trend towards more speed and deck armor began around 1914-1915, but was greatly accelerated by the battle of Jutland.

I don't know of a reasonable short form way to explain the armor interaction issue past that but the springsharp warship design program can let you do your own experiments with reasonable accuracy. Friedman's US battleships book is also an excellent place to read about the detail design processes that lead to this, it's expensive but most major library systems can get you a copy in the US. If you like battleships you'll love this book and it's very approachable as a text.

The problem with all the treaty battleships was 35,000 tons wasn't enough for a ship with 16in guns and armor against 16in guns and 30 knot speed, South Dakota came closest to this combo but all such designs were compromises. So they all gave up one thing or another, or several things, in an effort to mount a reasonable balance of guns, armor and speed.

At that point two quads uses the least weight, but means half the armament can be lost to one hit, the French quads had a bulkhead of armor down the middle to make this less likely. Nobody else would accept that risk. The French ship however had excellent armor. Four twins uses the most weight but most redundancy. Three triples weighed little more then four twins and gave the most gun barrels, but the worst distribution of fire.

So now we have three triples... why two forward?

The reason to have two turrets forward and one aft is two fold at that point. One is aggression, you can use the forward turrets while closing with the enemy, increasing your chances of winning an offensive battle. One reason the Germans stayed with the 38cm twin was they knew they had a smaller navy and might need to run away. They also indeed did not have a triple turret ready for this caliber of gun, but they really didn't want one either. Their H-39 battleship laid down with 40cm guns also still used twins. These ships were cancelled as soon as WW2 began.

In contrast the French all forward gun ships, and RN forward gun ships were built on the basis of 100% aggression. Though by 1940 the French had decided that the next quadruple turret ship was in fact going to move one turret aft, for equal fields of fire but slightly greater weight.

The other big factor is weight balance in the ship, the engines and reduction gears are aft and very very heavy, battleships, and even missile armed warships all tend to be stern heavy because of that engine weight. You want them stern heavy to a point so the bow doesn't plunge into the waves as well. This improves habitability of the ship and lets you keep up your speed in bad weather. Which can be an important advantage if you are trying to run down an enemy with similar speed in calm weather, or just get somewhere in the world in a hurry. This favors putting more main armament forward to maintain the proper weight balance without excessive displacement.