At a steady pace, on flat ground (no stop/start acceleration, or hills) Bike Weight and Rider Weight don't make as much of a difference as Speed WRT Calories expended.
Unless you are an unusually large person, or pulling a lot of extra weight, like a trailer or cargo bike, 12mph cruising doesn't take a whole lot of effort, but it does take some. Riding for an hour, your body does adjust to the effort expended. On your dutch bike, you are neither crushing big 52t gears, or spinning high 90rpm cadence, but it's more than just sitting in your chair. When you finish the ride, and sit down, your body is still operating under the 'high effort 'settings'' which is the 'exhaustion' you feel, as your body re-adjusts to 'at rest.' With better conditioning, your body will adjust faster, but it still takes time. This is why almost every training plan for any sport or activity includes warm-up and cool-down time.