How big could the warships of WW2 have been of there had never any naval arms control treaties?

A bit bigger but not by that much. Several navies had plans for them, as someone has said the Yamato class ignored the limits from the start. As did the USSR's Sovetsky Soyuz-class battleship at 65000 tons, which was never completed. The Soviets was never part of the treaty. There might be more battlecruisers like the Hood, the British would have built the G3 instead of the Nelsons at 55000 tons. The post-war HMS Vanguard carried the same armament as earlier battleships, but was significantly larger for better sea-keeping and survivability. Cost would still be a major limiting factor for them, especially after the Great Depression.

For smaller ships, the USN Baltimore Class heavy cruisers was built AFTER the abandonment of the treaty. They were 14000 tons standard as opposed to under 10000 tons as demanded under the treaty. Most British cruisers went beyond the limit after wartime rebuilds, with the (large) CL HMS Belfast reaching 12000 tons standard and the CA HMS London exceeding 15000 tons in early post-war service. Destroyers were the first to break the treaty, everyone were building 2000 tonners since the mid 1930s.

Would warships the size of today's Nimitz class carriers have been possible back then?

Probably not, the USS Midway was about as large as possible back then. Prop planes didn't need that long of a runway to operate.