Centre of Gravity
It is important to differentiate between the C.O.G. of the camera and the common C.O.G. of the complete inertial system (e.g. camera and the stabiliser).

Camera balance adjustment (horizontal displacement of the centre of gravity)
Camera balance is achieved when you horizontally position the common COG (of the stabiliser and the camera) so that it coincides with the line drawn vertically through the imaginary intersection point of the tilt and roll axis of rotation. At this time the camera's plane is parallel with the ground surface, as expected.

The common C.O.G. of the balanced camera can neither be in the intersection point nor can it be too far from the intersection point vertically, because in this case the torques of the two 'ends' of the stabiliser (i.e. the torques of the camera and the counterweights) would be so different that they would practically position themselves vertical anyway, regardless of the incorrect horizontal position of the camera C.O.G.

Drop time and Period
Drop time is the time it takes for the stabiliser post to first pass through the vertical after being released from a tilted position.

The period is the time it takes to complete one cycle, swinging to and fro.
Period = Drop time x4
The optimal drop time of stabilisers is usually from 1.5 to 2.0 seconds, so one period is from 6 to 8 sec.
The drop time (or period) is independent of the starting angle (e.g. the times can be considered equal at 20 or 40°), similar to a pendulum clock. (In practice, the period can be measured easier and more precisely.)
Drop time adjustment – Vertical displacement of the center of gravity
To achieve proper functioning with a horizontally well-balanced camera stabiliser, the common C.O.G. of the camera and stabiliser must be positioned from about 10 mm to 30 mm (from ~0.5 to 1.2 inch) vertically under the intersection point of the tilt and roll axis of rotation in such a way that when the counterweight of the stabiliser is tilted from its original (vertical) position and released, it passes through the vertical in a previously determined amount of drop time. This is the adjustment of the drop time, that is, changing the height of the common C.O.G..
For any distance value between the C.O.G. and the pivot point there is a corresponding drop time value, and so the C.O.G. height can be perfectly characterized and set by providing the drop time. Drop time can be measured more easily than the C.O.G.-to-pivot point distance, therefore in practice the drop time is usually provided for setting the C.O.G. height.

Dynamic balance
When rotating around the vertical axis, an otherwise statically balanced stabiliser's configuration is affected by different inertial forces due to different mass distribution and radially increasing tangential velocities. If these forces do not cancel each other out, they wobble the camera (and the stabiliser), this is known as the 'corkscrew' effect.
Low mode (vs C.O.G. position)
In low mode the C.O.G. is located toward the camera relative to the pivot point. In this set-up the stabiliser is flipped upside down.

When the common C.O.G. of the camera and stabiliser is vertically moved away from the intersection point of the axes of rotation, then out of the two masses (camera and counterweights) above and below the axes of rotation the one with the larger torque turns downwards. If the C.O.G. is higher than the pivot point during set up, then the camera turns to change places with the counterweight; this is the set-up for low mode.

Pan, Tilt, Roll movement
Pan: allows the horizontal rotation of the stabiliser (and the camera)
Tilt: allows the back-and-forth tilting of the stabiliser
Roll: allows the left-to-right 'side-tilting' of the stabiliser
Pan, Tilt, Roll damping
Damping is the resistance to the stabiliser's movement in separate pan, tilt and roll axis. As damping increases, more and more force (torque) is required for the stabiliser to rotate around the axes.
The damping control needs to ensure sufficient braking force throughout the entire payload range, otherwise the stabiliser can only be used for a very narrow load range.
If the stabiliser's damping adjustment is not ultra smooth, this will be visible on the camera movement, but excessive damping spoils the stabilizing effect.
Tilt & Roll Damping
If the tilt and roll damping is too high, the camera movement will deviate from the plane, in turn, if it is too low, the stabiliser will swing for too long.
Pan Damping
If the pan damping is too high, the camera will "schythe", in turn, if it is too low, the panning will be uncontrollable.

Payload capacity
The payload capacity of stabilisers depends on the total weight of the fully equipped camera and the camera's C.O.G. height. If the C.O.G. height increases, usually the load capacity decreases.