Like newbury said, a lot depends on what you're using with the tractor and what your land is like. I'm a skittish newbie (~ 35-40 hrs. seat time in my life) with some pretty steep land and I want to get that center of gravity as low as I can. Plus I have a front end loader and no backhoe, so again, I need weight in the rear; even with 4WD I can't get up hills with a load in the bucket without some weight in the rear.
Plus my owner's manual recommended filling them; so I did, and yes, it made a big difference. There are other ways, though, like weights, or
ballast boxes hung off the 3 point hitch. Thus you can "simulate" the effect of filling your tires to see if it would make the difference that you require.
It's not ALL about weight in the back, it's more about balance. Too much weight in the back can be bad, too. My owner's manual had a recommended weight distribution, I forget what it is right now, but yours might as well.
I also keep my mower deck slung beneath for the most part. Again, it lowers the CG slightly and is a fairly well balanced "ballast."
Like the guy said, do a search and you'll find this subject hashed out in minute detail.
But if you do fill, I think there's this stuff called Rimguard that doesn't rust your rims like calcium chloride & other stuff can.