That's interesting because, according to the Schwalbe website, they're both the same weight.

No.
The added effort required to accelerate a heavier tire is equal to the added effort that all types of drag needs to put forward to slow the tire down. Your speed will fluctuate less quickly meaning less need to re-accelerate.

You misunderstand what 'acceleration' is - it is actual change in speed caused by an imbalance in forces on a body, not just 'any force' applied to the body. If you are putting 200 watts into turning the rear wheel, and all combined drag is pushing against you with 200 watts, then your acceleration is zero, so there is no effort required to accelerate the wheels.

If, in the same scenario, you are unable to maintain a steady 200 watts for some period of time, you will decelerate more slowly if you have more mass and so you will need to accelerate less than if you had less mass to get back up to your cruising speed.

Different or wider tires might have more drag, and any added mass will require more energy to be carried up a hill, but your statement about heavier tires requiring more energy due to 'constant acceleration' is false.

Weight has very little to do with it. A supple casing, especially if used with a thin tread requires less effort to roll down the road. But some tires have a stiff casing, or a thick tread, or a layer of soft rubber that consumes a lot of energy as you flex it, those tires are slower.

When you are rolling down the road at 13 miles per hour, you are flexing approximately 20 feet of tire casing on each your front and rear tires during every second. If that is not a very flexible tire then that consumes a lot of energy. I have some older Schwalbe Marathon Dureme tires, that model is now discontinued., They are size 26X2.0 and were sold as a durable touring tire for rough areas and poor quality pavement. For a thick treaded tire, they roll quite well, in part because of the supple sidewall and casing. Later I thought I was buying another one of the same tires on-line, but this one was one of their tandem rated tires and I did not know that until I received it. (The Dureme came in both a solo bike version and a more robust tandem bike version.) The tandem rated one had a very stiff sidewall and stiff casing. Both tires look the same, both are the same size. But the tandem one is very slow compared to the other one.

Heh, I put my fat bike into a personal top three strava spot on one of my local MUP segiments last week, if we want to get into fatter tires and speed. An anomaly for sure, but humorous nonetheless

Which I suppose befs the question a) whats the rest of the differences between all the Marathons, and b) why name them all similar!

I think you're mistaken in saying "hey, 2, 3, 5mm is not that much". Consider the % increase in widths:
35-37: 5.7%
37-40: 8.1%
35-40: 14.3%

Consider the contact patch. Let's assume it's a square (and it depends on the rider weight, tire pressure, etc.) - now we're dealing with squaring:
35-37: 11.8%
37-40: 16.9%
35-40: 30.6%

That contact patch lets you run at a lower pressure but also probably results in a more tire deflection. If we were to calculate the 'trivial volume' difference in percentages, it would also be quite large.

Bingo. IMO, if you're already moving, then you don't need to worry about acceleration all that much and air resistance is negligible given the surface area of your body plus your gear. But if you're working against a soft tire which is deflecting a lot, you're expending more energy to go the same speed. Yes, you can be fast on thick, flexible, or knobby tires, but the question is does it make you more tired in the end? A stiffer, thicker tire can ride as well or better than a soft, thinner - or underinflated - tire.
Tourists don't usually use power meters... so you wouldn't know it in the field. but if you wanted to do an experiment, take the thicker, flexier tire and do a 3-5 mile ride at, I don't know, 150 watts (or whatever round number you can hold that long). Then switch to thinner tire and under the same conditions repeat the ride with the same wattage. Compare the speeds. Or do it backwards, ride at the same speed and compare the wattage.

Bigger = Better, IMHO. Currently running 29er 3.0 and 2.6 tires on the Karate Monkey. Big guy, full load, cushier ride. This summer my travels will see all kinds of riding surfaces, dirt, single track, dirt roads, gravel and pave. Last year I used the geax tattoo, a sort of slick that were 29 x 2.3, great tires.

+1 ^^^

I find 26x1.75 a good all-purpose tire, 26x2.0 good for off-pavement, otherwise rotating mass/pedaling effort penalty. On pavement, unloaded, 26x1.5 is sweet spot, while anything < 26x1.4 has significantly shorter lifespan.

Actually, if using the same pressure, tires of identical size will have to deflect a roughly identical amount to create a contact patch the correct size to hold the same weight, so a tire with a thicker tread or casing or flat-resistant layer will almost definitely use more energy and give a rougher ride than a thinner more flexible tire.

Of course, if you are using lightweight tires and get seven flats per hundred km, you will be much more comfortable and less tired using a tire with flat protection, but for reasons other than 'ride quality'.

more tire bounce?

I think the bigger question is what kind of surfaces will you be riding on and how much weight are you carrying. My salsa marrakesh came with 40mm marathon pluses. changed them out for a few different types of tires due to they're weight. I only use 38, 40mm tires right now. I recently finished a 6 day 900Km tour in Ontario and my ride had a mixture of good pavement, really bad pavement and, and about 100Km of gravel. There were a few times i wished i had bigger tires. the 700x38 tires i used held up but i really think that a 40, 42mm on the right rim would be the best option. Going for light weight while touring to me is kind of silly. I don't want a puncture going down a rough hilly road loaded down. Touring isn't supposed to be fast anyway

True. I was thinking about getting some Almotions (38mm) but was put off because of the weight, but if you say they're noticeably better riding than Mondials, then I might reconsider.

This spring I did several Randonneuring rides of 300-400 km (in one day) using Rat Trap Paas tires (26 x 2.3) and my experience was that they may feel slow, but in fact on pavement they are not slow at all, whereas on rougher surfaces they are a lot faster than thinner tires. The guys I was riding with are usually a lot faster than I, but on the rough surface they could not keep up; they were riding 38mm and 42mm tires.

Of course Randonneuring is not the same as touring; and not every tire is as fast as a Rat Trap Pass; but I'd say there is no downside to such a fat tire.

For what it's worth, I have not found those tires to be prone to flats, either; rather less so than other tires on my experience.

Nah, it's far more kickass, and if theyre used there I've got no leg to stand on complaining

Well, I should add: I'm an outlier. I haven't seen anyone else riding such fat tires. Most riders still subscribe to the idea that a thin high pressure tire is faster, and it's hard to persuade anyone to the contrary. Thin high pressure tires definitely feel faster, and that's often all it takes to convince people.

Jan Heine has made a diligent attempt to test different tires in an objective way, and (predictably) people question his methods, his results, or even his motives (he is in the business of selling expensive tires, after all).

I don't know. All I can say is: I have not found fast fat to be a disadvantage.

I have enjoyed my 26 x 2.15" Almotions as tubeless tires. They did feel heavy and stiff to me when I was putting them on, but I feel like running them tubeless helped, and I've been happy with them, but if I found another tubeless tire with similar size and tread, I'd be willing to try it. If I were going back to tubes, I think I'd switch back to the Big Bens that the Almotions replaced.

I'm one of the lucky or unlucky few who have a pair of Dureme tires. Can you please share how I might understand whether or not I have the tandem version? Because I have a tandem. Thanks.

Mine says Tandem Ready in red on the sidewall.

Well then. I guess I'll leave them on my single bike. Thanks for the information. I guess they're just slow. Oh well. My 700x35c Clements were worn out but I waa never in a hurry, anyway. I use the tire liners that only recently caused a leak in the rear tire. I put the 700x40c Duremes on to replace the Clements.