Loading your tires will result in a rock solid platform adding stability and traction. Two things you can't get enough of. Most guys load the tires with the valve stem up, at the 12:00 o'clock position and then fill them to the valve stem level. This will reduce "sloshing" a bit, but give you more fill and the above results.
Cons are if you ever have to replace the tire it is a bit more trouble and also weight for finished groomed lawns. But I see that is not a concern of yours.
There are several fills available, depending how much of an environmentalist you are and how concerned you are about a leak or how it affects your rim.
Calcium chloride is the staple of old time farmers as that offers the greatest increase in weight per gallon.
Beet juice, windshield wiper fluid, water and anti-freeze are also common fillers.
I have all 4 of my tires filled with anti-freeze and water. I run tubes in my tires. The difference between filled and no-filled tires is substantial. If you've run your tractor non-filled, then you will feel the difference and can post after you do it as a testament.
A
ballast box is used to help shift the percentage of load more evenly over your tractor's axles. So when you have a heavy bucketful, a ballast on the rear will make your tractor more stable, acting like shifting the load from mostly over the fronts toward the rest of the tractor. Your tractor will handle better and have better traction, etc.
Here is a handy chart to tell you how much weight you can achieve:
Liquid Tire Ballast
And this one to tell you more about filling tires and ballast:
G1235 Tractor Tire and Ballast Management, MU Extension
They are both good information.