On the point of which side to carry such as a side mount mower...if I am wrong am sorry...I will stick with load on lower side on this reason, if load in on the uphill side and it starts tipping as the side load gets higher it will help roll you down hill more so than just the tractor by itself. I believe you will find it will speed up the roll as that weight moves higher up. Now I may be wrong there. But this I am 100% sure of, if the cutter's weight is the tip reason and it is on the down hill side and not high in the air as soon as it hits the ground the tipping probably will stop. If on the uphill side and it begins to roll it will roll.
Want to try this in a safe manner, if you have an excavator load it to the max, with bucket run all the way out over one end of it, but only say a foot off the ground and your excavator setting on level ground, slowly rotate the excavator. As you rotate to the side you probably will find the machine wanting to tip and it may very well tip but the second the bucket hits the ground it stops. Why? Because the weight causing the tip was removed from the machine and transferred to the ground. DO NOT DO THIS but take that same load and raise it as high as you can and run same test. Because you have the load so high when it begins to tip the machine probably has so much energy behind the tipping it will most likely continue the tipping action. Ok just go on youtube and watch them. If you could find a video of how a company test the tipping of a crane made to tote a load you will easy see this, same thing with heavy loaded FEL and bucket in the air and you hit the brakes. That is why even here keeping the load low is mention over and over. I worked for a crane manufacture for 10 years, in that time frame worked in many areas but one job I did on occasion was to test load the machines. We loaded them like 110% of stated capacity and then had to run the boom out to where the load tipped the machine. We were trained to keep the load like a 1 foot off the ground at all times I'm the tip test. It never failed when the weight hit the ground the tipping stopped. Now if it was say 50 feet in the air, I would bet the machine rolled.
I will agree if you have a light weight piece of equipment on the down hill side compared to the weight of the tractor and it begins to roll the equipment may be weak enough it can fold up. But that is a tip caused not be the equipment but tractor or hole.
One other crazy reason to me if you are going to run a cutter high in the air I rather have it on the downhill side is I rather have my tractor roll onto it than it fall on tractor with me in or on it. Did not go back to my post but if I did not mention counter weight for down hill implement meant to. If you place cutter on uphill side do you counter weight or not?
I am far from perfect, if anyone disagrees would like to know what is it based upon. kt