I always mow with the loader off (BX25 with MMM). Reduces the weight, keeps me from hitting stuff, and increases maneuverability.
The only time I might mow with it on, is when I'm cutting a slope head on
(straight uphill), and the weight of the loader helps to increase traction of the front tires.
My mowing has a lot of slopes to deal with, and I find the BX to be more stable without the loader.
Even if you keep the bucket down as low as you can, I find you are still raising the center of gravity of the whole rig, since the pistons and lever arms of the loader are heavier than an empty bucket, and those are higher than your normal center of gravity.
I've only seldom felt "tippy" with the loader off, but it happens more frequently with the loader on.