this is me speculating... foam tyres are the lightest, but they kinda need a really neat runway otherwise they get chunks chipped out of them, also they have more resistance when you are rolling on them, but they are not prone to being stretched into a pizza cutter shape by the centrifugal force when the wheels are spinning really quickly

smooth rubber tyres are tougher, heavier , and offer the least resistance , and you can use them on many surfaces....

the treaded tires are there for looks i guess, the treads hammering the ground will slow it down, also there is a possibility that the treads could pick up debris from the ground and fling it at the underside of the fuselage

the weight of the tyre is important not only in-flight, but also at the instant that you touch down, the tyres will have to suddenly be spun at the groundspeed of the plane, the lighter it is the easier it is to do so
or am i wrong on any of these points?