..the aim is to get the CoG as low as possible. You do what you can to reduce weight transfer, to get the most benefit from all four tyres. Low CoG is the starting point.
On a bike weight transfers are *massive*, the CoG is inherently high and can move about, so it's all about controlling it. The CoG has to be in the right place. The 'right place' depends on the bike - its purpose, its size, its mass, available grip...
Without writing an essay on bike dynamics (which allows me to neglect Moments of Inertia, steering geometry, spring rates and damping, tyre widths, chain to rear pivot location) CoG effects can be summarised as
Longitudinally,
A low CoG will reduce the weight transfer onto the front wheel under brakes, with a tendency to push the front tyre. (think of cruisers)
A low CoG will reduce weight transfer onto the rear wheel under acceleration (look at drag bikes)
A high CoG will have more weight transfer, with a tendency to want to lift the rear wheel under brakes
A high CoG will have more weight transfer under acceleration, wheelie time (think how easy it is to pop the front up on a dirtbike)
Transversely,
a higher CoG means less lean angle for a given speed and radius of turn (sounds wrong, but isn't)
Of course, the CoG on a bike is heavily influenced by rider positioning - a big mass sited a few feet above the ground - which is why you see riders clambouring all over bikes, this is to get the weight where you need it. Back wheel lifting under brakes? move back in the seat to get more weight over the rear. Front wheel not turning in? Hunch over the handlebars to get some weight on the tyre.
The above can be summed up as: ratio of height of CoG v Wheelbase. Long and low, stable. High and short, twitchy.
This isn't just from theory, ride a Harley
Next up, does a light bike go around a corner faster than a heavy one?