To calculate the location of the center of gravity (CG) of a robot, we can find the approximate centroid of the different subassemblies, such as the frame, a ramp, the motor/transmissions, the battery, the manipulator assembly, etc. Each of these can be viewed as acting as a point of mass, and the distance of this centroid from some axis, times the weight of the subassembly, gives a moment that we can sum (keeping track of +/- signs, depending on which side of the axis it is on). We can then divide the sum of the moments by the total weight, to find the distance of the CG from that axis.
There are three different axes that we need to worry about. The first two are the distance of the CG from the side to side center and the front to back center of the robot, and other is the height of the CG from the floor.
The drawings show a generic robot, with a CG located towards one end, a little bit to one side, about a foot and a half above the floor. The diagonal lines show the "tipping angle". When the CG goes past the point of support, either to the front or rear or one side, then the robot will tip over. How far does your robot have to tilt to reach the tipping angle? If it only has to tip a few degrees, then you are probably going to see it laying on it's side in a significant number of matches. If the CG is down low, and centered, then the tipping angle is very far from being vertical, and your robot will stay upright most of the time.
The robot does not actually need to be pushed over by another robot to reach the tipping angle, because of acceleration. The robot's center of mass is also it's center of inertia when accelerating. If you were to apply a driving force as shown by the arrow, the robot will be twisted around the CG, and could easily "do a wheelie" and tip over.
So, it might be worth considering putting most of your weight reduction efforts into the "stuff" that sits up high on your robot, and leave as much weight as you can in the drivetrain/chassis. Also consider the location of small, heavy items such as the battery and air compressor, which could be moved around to balance the robot from side to side or front to back. Think about how the wheelbase and track width affect tipping.