You asked a couple of good questions.
I would run with the weights in a raised position. Less chance of bottoming out if crossing a ditch or depression. The difference in height of where the tractor carries the weights is negligible in the case of stability. Before I get flamed for that, if the high point was above the wheels it would begin to have an effect. Also it would have to be a significant amount of weight that is probably more than most of us carry on the tractor. A few hundred pounds mounted on a weight bracket on the back will not change the stability of the tractor in normal operations. Raise the weight up and do your work. A good precaution is the keep your head on a swivel while operating the tractor. If you will be operating on a slope that seems to make you uncomfortable, lower the weights or drive up and down the slope instead of across it. If you get a feeling of uneasiness when operating, stop and check your surroundings and conditions. Trust your instinct. As far as the next question, lower the weight. This particularly true if it is being supported by the hydraulics. No need to have the extra weight hanging on the tractor at rest. Also even more important is from a safety aspect. In all almost all equipment and almost all instances, standard practice is to release the hydraulic pressure and lower the load to a resting position.