To the point of ruts in a soft lawn...yeah, it happens.
My first tractor was the cub with loaded ag tires and wheel weights. I dragged a finish mower for the lawn. All in all, not bad on marking up the lawn.
My next tractor was an 15 horse diesel Bolens with no weights, no liquid, turf tires and no marks on the lawn.
Next was the 28 horse Cub Cadet with turf tires, no weights and no liquid. No marks.
Now it's a B series Kubota with Rim Guard and R4 tires. Marks the lawn like a champ, I'm afraid I think it's as much a matter of the weight distribution to the tire tread, though I'm not sure. However, I need the weight and prefer the R4 tires to do other work I now need to do, so I deal with the marks on the lawn--and wait until it's dry when I can.