weave is associated with the rear of the bike self steering, this is caused by loadings on the rear suspension, the unsprung mass damping and the length of the swing arm.
wobble is due to the front fork rake/ caster angle front suspension type damping and headstock bearings.
Change the bikes CoG and this can have serious effects on the possibility of both occurring.
Both occur naturally on a bike but the design and construction are made to reduce this from the start. Install a fairing or fixed luggage and you can dramatically alter the characteristics of the bike. change the airflow over the rear of the bike can alter the loading on the rear suspension and off load the swing arm, thus reducing traction nad increasing weave. decelerate and the bike loads the front fork increasing the spring pressure. incorrect damping can cause the suspension to unload and the rake angle then changes, then causing the bike to wobble.
When cornering the two wheels travel on different tracks the rear wheel is on a tighter radius than the front hence counter steering ( see cinder track racing) increase the lean angle increases the degre of counter steer and the rear wheel starts to drift. expert racers use this to their advantage. on exiting the corner ( past the vanishing point) the rider throttles up unloading the front suspension but loading the rear when it is still in a slide. the sideways action and grip cause the bike to weave until the damper catches up and equalises the loading front and rear. incorrect steering damping at this point can lead to a tank slapper of a wobble of the handlebars.
Motorcycling is the use of certrapetal force as opposed to centrifugal force.
Dont forget the engine either. inline engines that run fron front to back as per Triumph rocket BMW twins Guzzi's etc they produce latteral forces in translation that are rotational about the axis of the crank at 90 degrees to the crank. IE the engine rotation causes the bike to respond by either turning into the acceleration or out if it. Transverse engines GSX CBR bandit Blade Fazer etc have the same rotational force but this relates to movement from either left to right of the bike so throttle responce causes the bike to tilt over.
additionally single sided swing arms also have an impact if the swing arm is on the lefthand side of the wheel the bike will fall into left hand bends and try to climb out of righthand bends.
As such it bothers me why manufactures who make transverse inline multis don't have contra rotating crankshafts with single sided swing arms as this will equalise the forces exhibited on the bike. BMW have taken this on board but they still haven't got it completly right yet!!!
Riding a bike is like flying and is more akin to a helicopter than a plane or more precisely more like flying a plane with a rotary engine as opposed to either an inline or radial engine