Okay WW1, but HMS Furious - a "light battlecruiser" at around 20,000 tons displacement - was meant to carry two 18" guns in single turrets, fore & aft. Only one was ever fitted, and firing the gun shook the ship so badly things broke. So I'd be prepared to sat 20,000 tons is about the low end for mounting 16" guns on a ship designed to do things, not just be slow floating artillery confined to shore waters.
With WW2 tech, I suspect it could be made more strongly, faster, and somewhat smaller, but with pretty much the same displacement. Personally I'd go with a single twin turret forward, Nelson style, to allow a shorter hull with broader beam.