"just out of curiosity, why not?"
Bird, I chose not to weight the tires because I didn't want to deal with the mess if I got a flat. I also have lots of thorn trees around here. I've plucked a lot of thorns out of the tires, but so far, have been lucky that none of them made it all the way through the R4's. Also, I've been restoring a lawn tractor with rusted out wheel rims and really don't like the idea of introducing liquids into the tires on purpose. I realize that things like windshield washer fluid and beet juice aren't supposed to be corrosive, but I still don't like the idea. Not saying I'll never do it, but I'm trying to avoid it.
I don't have the spec's close at hand right now, but I didn't see much difference in weight on the 72 inch mowers. As I remember, even the GM1060 was only about 65 lbs less than the GM1072. Seems like you'd have to drop about 200 lbs from the weight of the mower to make much difference. I think the GM1072 that I'm running weighs 678 lbs or so.
On edit, I see that the GM2072R only weighs 600 lbs, so that might be enough less weight to make a difference.
How much does your BEFCO unit weigh?