It's more about soil, moisture content and tires than other things. I live in clay soil that is like a wet sponge in the spring and blacktop in the hot and dry summer. I have mowed with a 30HP, 1,700lb
B7800 Kubota pulling a 7 ft Woods mower and I have also mowed with a 90 HP, 9500 lb Deere pulling the same mower. Either one can do serious--or zero--damage depending on conditions.
Stay off the ground when it's wet or damp. Period. Wet will rut to varying degrees so stay off. Better yet, anticipate the rain and mow in advance or wait it out and deal with it. Mow at 3 1/2" and you wont have to rake anything, ever and can wait until it's dry.
No circling turns around trees in the Spring and almost no turns unless wide and sweeping. Industrial tires--or maybe turf.
Now, when it's hot and dry in July. August and maybe September, I saddle up the big Deere and have my way with the lawn. No real sharp turns, of course, but no ruts, no damage and no nothing. It just works like a champ. In the wet Spring, a bicycle will do damage while in the dry summer I could probably do donuts with my truck and not have a problem.
So, more than the size of the tractor it's how you use it and what kind of tires are on it.