With my CT225 (same as a CK27, I think) running about 3,500 lbs with the loader on, I have no trouble moving 6' round bales on the three-point. I wouldn't try it with the FEL unless I had way more ballast than I currently do. The round bales weigh in around 1000 lbs, so if the tractor was only down around 2000 lbs, I would hesitate a bit, but probably still go ahead, carefully.
I will say that the additional weight would be a real down-side if I wanted to use this tractor primarily as a lawn-mower. I will bush-hog a pasture all day long with this thing, but I wouldn't take it on anything I wanted to look nice if the ground was even the slightest bit wet, and even with dry ground, I make tracks that take weeks to grow out if I go over the same ground more than a few times in a row. I can see that a lighter tractor in the same power class would be nice for a mowing application. They say you never regret getting a bigger tractor; I wouldn't say that I regret my purchase, because I love my tractor, but mowing is a big part of my property maintenance, and it's a shame that I can't do it with my biggest and best tool. But if I had gotten a smaller tractor, I know there would be other things I would regret not being able to do, so it's six on one and half-a-dozen on the other. As it is, I am marginal with a box blade when I get into really heavy clay, and I sometimes find myself wishing I had another thousand pounds and fifteen HP. The day somebody makes a tractor that will pull a three-bottom plow and mow around trees without crushing a single blade of grass, I'll buy it!
OP said finish mower, but in the original post, mentioned rotary cutters. I think the finish mower reference was a typo.
Your tractor is capable of lifting a round bale with the FEL. Throw a heavy implement on the back or even another bale. I saw a picture the other day of a BX lifting 4x4 a round bale. If you have fluid in your tires your tractor is in excess of 4,000 pounds.