The CK35 comes in around 3000 lbs, which is more or less the same as my CT225. I have R4 (industrial) tires on it. I would hesitate to use it as a full-time mowing machine, especially if I had a nice lawn. If the ground is wet, it will leave scuffs--no question. I just don't use it if it's been raining, if I can possibly avoid it. If the ground is dry, you might get away with it, although I still see the marks if I make repeated trips over the same area. Given how much of your work is going to be mowing, you might consider getting turf tires. Some people say that chains on turf tires are actually better than R4 (industrial) or R1 (agriculture) tires. You may end up giving up a little in loader capacity due to the lower weight rating of the front tires (ask your dealer), but it'll probably be worth it for you.
Frankly, I think that 3000 lbs is about the upper limit of what one should consider for a mowing machine, but I would defer to others who are more experienced for final opinion there. If I was going to be bush-hogging or haying pasture, that'd be another story.
Whether you go with a belly mower or a three-point rear finish mower is a question you should consider. The belly mower is easier to get into tight areas and maneuver around, but a three-point mower is going to be a winner in a lot of other ways.