Im not sure about this but I imagine that the thicker heavier swords were produced just before the Edo period when the country was in civil war for most of the 16th century. Muskets had been introduced from portugal and therefore very heavy "bullet proof" armour was being worn. Swords also had to be adapted to be heavier and have a wider edge that was slightly blunter and would sustain atttacking this armour better. I believe Dotanuki swords are a prime example of this. A very heavy katana with no frills fittings intended for heavy cutting in battle.
Ive got several books and leaflets from the imperial sword mueseum in Tokyo upstairs but Ive got an interview to get to now. I'll look them up tommorrow and clarify the dates and stuff