Sunday's word length slots in nicely between Thursday & Friday, which matches what I've read the NYT editors desire (for Sunday to be "roughly as difficult as t

Sunday's word length slots in nicely between Thursday & Friday, which matches what I've read the NYT editors desire (for Sunday to be "roughly as difficult as thu/fri") ... and gainsays your hypothesis =) Rather than the set of possible answers being U-shaped, maybe it's a size thing: it is hard to fit in N medium-sized words unless you have the extra space of the Sunday puzzle. The top & bottom of Fri/Sat puzzles are often split into just two words (one long, one short), this might inform our developing hypothesis.