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.