It has bees said that loaded tires put stress on the outriggers and makes the tractor harder to move around, I have loaded tires "Rim guard" and a BH no problems.
My dealer told me it's not a problem other dealers and people will disagree, it was offered free when I bought it new so I went for it.
I guess lifting the back end off the ground with the extra weight is why some say it hard on the riggers, also when trying to move the tractor over your ditch the extra weight makes it a little harder on the hoe.
My BH is on the tractor about 50% of the time so its nice to have the extra weight when it's not on.
Like I said I don't have any problems.
The owner's manual for my BX-25 advises you not to load the tires with the back hoe. When I plowed snow in the wintertime using a rear blade, I used a second set of loaded rear tires. I was able to find a gently used set in the local classifieds for this.
My B21/BT751 manual recommends rear tire liquid ballast but says it should be removed when the backhoe is in place. Oh yeah, right! Who is going to add and remove liquid ballast?
The added stress on the stabilizers should be small in comparison to the added load when digging with the backhoe, IMO.
I used loaded tires for many years on my L3010, L3430, L6060 and MX5800 with BH90 and BH92 hoes. All the tractors had R4 tires which weigh more than R1's. I can't speak for hoes used on the B series Kubotas but the stabilizers on the BH90 and BH92 hoes lift the tractors with loaded tires completely off the ground. I never had any problems.