General rule for rotor design: for a given weight of the rotor try to put the mass towards the rim. That is: make most of the rotor thin, as thin as possible while still providing sufficient structural integrity, allocating mass to the rim.
As to whether a heavier rotor provides benefit:
Take the case of a spinning top. When you have a spinning top that is in precessing motion: the torque on the spinning top is due to the top's own weight. Making a spinning top heavier offers no benefit. The torque on the spinning top and the torque countering effect from the gyroscopic precession are both proportional to the mass of the spinning top, so there is no net gain.
It's a whole different matter when the gyro setup is not used to stabilize itself, but something else.
For luxury yachts there are large devices that use gimbal mounted gyro wheels to counteract roll of the ship. The gimbals of the gimbal mounted gyro wheels are moved with very strong actuators.
In that application the gyroscopic effect has to be strong enough. In harbour the bow wave of a passing ship tends to make other ships roll. The gyro stabilisation system can counteract that. The bigger the ship, the bigger the gyro wheels need to be in order to exert sufficent force.
I'm guessing the video with a device with nested rings, powered electrically, was a video showing the mechanical gyroscopes that were used onboard the Moon landing spacecrafts.
The bearings of the gimbals can never be perfectly frictionless. For the high accuracy demands of the spacecraft navigation the bearings had electric assistence. When the spacecraft would begin to move (due to thrusters being fired) there were sensors registering the motion of the gimbal relative to the gyro wheel and a small electric motor would provide some assistence, calibrated to precicely cancel out friction of the bearing. Without that canceling even the minute friction of the gimbal bearings would have an effect on the gyro wheel, slightly changing its orientation. The assistence kept the drift of the navigation gyro within specification.
As to how gyroscopic precession works:
There is a 2012 answer by me in which I discuss the mechanics of gyroscopic precession The discussion that I present there does not use the concept of angular momentum vector, nor does it use vector operations such as vector cross product. Instead the discussion capitalizes on symmetry.