The South Dakota looks massive when compared to the Tennessee and Pennsylvania
Something like 80 feet difference or so if I remember right- but only a couple thousand tons heavier. Advances in engine technology in particular, as well as the novel (if cramped) idea of putting the boilers above the engines rather than in-line as with most ships, kept the SoDaks pretty short compared to contemporaries like the King George V or North Carolina. Which was the idea- a shorter ship means a shorter armor belt, and that's where most of the weight is on a ship like that.
BuShips built very good, if flawed, ships in the North Carolinas, and the idea to design a triple-16 inch mount that fit in the space intended for quad-14s allowed them to upgun during construction- a very good move. But as with most American ships, they were designed to be armored against their own shellfire- in this case, against 14-inch shells. So the plan for the follow-ons was to armor against 16-inch, but keep in the treaty limits, and so weight had to drop somehow. Reducing the length but increasing the thickness of the armor was key, and to do that these became very cramped ships. Note that postwar, there were some plans to heavily modify North Carolina and Washington into landing ships and such, but none were ever considered seriously for the South Dakotas.
(Also, amusingly, the British had the same idea with the King George V- just in case Japan broke the rules, they included an easily-changed feature to improve the ships past the treaty limits. Where the Americans designed a way to get bigger guns, KGV got an extra strake of armor, making her impervious in theory to 16-inch fire. Certainly in their only situation where one took heavy-caliber shellfire- Prince of Wales against the Bismarck- the belt never really was tested, so it's hard to say how she would have stood up to it. Then again, the South Dakota was the only American to really get its armor tested, and same result- only one major-caliber hit was scored, which was stopped by barbette armor rather than the belt.)
Really, the North Carolina and KGV make for a fascinating comparison- a duel would have been very interesting.