In Japan you travel better with less. The rooms in business hotels are small, the trains are full at rush hour and every change of city means carrying everything up platforms and stairs. Three resources let you bring half the luggage:
Takkyubin: door-to-door luggage forwarding
The takkyubin (or takuhaibin) is the courier service the Japanese use to send suitcases from one hotel to another. You arrange it at your accommodation reception or at any konbini: for 1,500–2,500 ¥ per suitcase they pick it up and deliver it the next day at your next hotel. It is ideal for the Shinkansen legs or for arriving at Hakone with just a day pack while the large suitcase travels straight to Kyoto. Send it with a day's margin: it is not same-day delivery.
Laundry: wash mid-trip and bring clothes for a week
You do not need to bring clothes for the whole three weeks. The coin laundries (self-service launderettes) are in every neighbourhood and many hotels have a washer-dryer on the floor: a full wash with drying costs 200–400 ¥ and takes about an hour. Washing once or twice during the trip lets you pack for 5–7 days instead of for the whole trip, which completely changes the weight you carry.
Lockers in stations for day-trip days
The large stations have coin lockers (300–800 ¥/day depending on size). They are very handy on the departure or arrival day, when you have already checked out but want to make the most of the day without your suitcase in tow.
The large luggage rule on the Shinkansen
Since 2020, on the Tokaido, Sanyo and Kyushu lines, luggage whose three dimensions add up to more than 160 cm (a large checked suitcase) needs a seat with space for oversized baggage, which is reserved free when buying the ticket. If you bring a suitcase of that size without the reservation, there is a 1,000 ¥ fee on board. The measurement is the sum of height, width and depth including wheels and handle; if you travel with cabin luggage it does not affect you, but it is worth knowing when reserving a seat with a JR Pass.