So while your question is perfectly fine there was some bad info given. In that there were several treaties limiting the size of warships, but that the Montana's were not impacted by them!
The treaties. After WW1 it was widely acknowledged that the dreadnought race, particularly between Britain and Germany was a contributing factor. And that building ever more expensive and larger capital ships would both increase tension with each new launch, and potentially bankrupt nations struggling with war debt. In 1922 then after a conference in Washington brought together the major naval powers of the US, UK, France, Italy, and Japan to address the concerns.
From this came the Washington Naval Treaty, which among other provisions included the limit of 35k tons on battleships you mentioned! It also fixed a ratio of tonnage at 5:5:3 for the US:UK;and Japan, this ratio was helped made by signals intelligence to know the worst deal Japan would accept. This seemingly second class status also helped increase resentment in the Japanese public as the treaty also required a 10 year halt on new construction except for certain provisions to replace existing ships, and limiting main armaments to 16in. The 3 major signatories all scrapped ships under production and designs on the table while also using a provision to convert some unfinished ships to aircraft carriers, the US converted 2 unfinished battlecruiser hulls to the carriers Lexington and Saratoga while the IJN got Kaga and Akagi along with setting some general other restrictions on the type and arms of warships built under the treaty. The first reaty battleships, the Nelson class, owe their 16in main armament to an exception made to allow each main nation 1 class of 16in armed battleships, and unique design to a desire to maximize armor protection over as small an area as possible to save weight, and built on designs proposed for ships prior to the treaty like the N3 BB or G3 BC.
In 1930 then the parties met in London to follow up on the treaty system building on a previous effort in Geneva. This treaty extended the ratio limits and set tonnage allowed for newly defined Heavy (guns of 8in) Cruisers, Light(guns of 6in or less), and destroyers and subs. Then in 1936 came the Second London Conference to again extend the system. Japan however walked out as it was already in the process of aggressive expansion and had in general sought every means to get around the treaty restrictions in many ships. However the remaining signatories, mainly the UK and US, sought to make it work, in particular retaining the 35k ton individual ship limit, and now a 14in restriction on main guns, but with an escalator clause to push it to 16in should Japan not sign the new treaty. When that came to pass the new US battleships of the North Carolina class were able to be adjusted for the new guns, however the British King George V class were not and were constructed with their 14in guns. The follow on USN design in the South Dakota class still adhered to the tonnage limit and were essentially North Carolina's that traded some speed for being armored to resist shells equal to their own.
The post treaty battleships. The Iowa class then int he late 30's was still very much in the early stages of design. However a major factor was achieving a higher speed than the previous 2 Treaty classes. Thus a provision which treaty powers were allowed to use allowed them to ignore limitations if non signatories began building ships not in compliance with the limitations, namely the Yamato and Bismarck classes then early in construction. By stretching the hull, avoiding adding more armor, a newer lighter gun design, and adding 10k tons the Iowa's could reach 33knots, while the USN wasnt exactly thrilled it took that much just for 6 knots it was still an improvement and the ships ordered. A main motivator in the design was the fear of Japan's large number of very large cruisers, hence early designs even shaved off some armor for extra speed or guns. Japan's main battleline was even older than the USN's and while it had some very good ships it was outnumbered and had only begun a single new class of battleships whereas the USN would have 3 at once under construction and 12 shisp ordered under the Vinson and 2 Ocean Navy acts.
By the time it was appropriate to begin work on the Iowa's follow on the Treaty system had broken down completely with the coming of war. So all bets were off and funding had already begun to be set aside for the ships. With more info and rumors of the size of the Yamato's filtering out something truly massive would be needed to fight them. Enter the Montana adding additional armor, and a 4th turret to the Iowa and sacrificing speed it would not be as good a hunter and couldnt work in concert with the carriers easily, but would be the equal of anything Japan was building as the design bloated from 45k, to 58k to nearly 70k tons. The main size restriction then was that it could not fit through the Panama canal as all USN ship could at the time, but the US had developed plans immediately pre war for a new set of locks to expand the size limit which the Montana if completed could fit through.
As a caveat we should also note other naval treaties occuring in the interwar. Namely the Anglo-German treaty which set a 35:100 ratio of the new rearming Kriegsmarine to the ROyal Navy. ANd in particular accepted construction of new U-Boats.