Here is a free body diagram of the forces on a motorcycle while leaned in a turn.
This is a rear view of the bike as it turns to the right.
The big dot is the bike's center of gravity.
It shows how the lean angle is determined by the radius of the turn and the speed of the bike.
There are two opposing torques, both of which share a "hinge" which is where the bike's tire meets the road.
The counterclockwise torque is the "high side" torque.
Its force is proportional to V squared over R.
Its moment arm is proportional to the cosine of the lean angle.
The clockwise torque is the "low side" torque.
Its force is proportional to G (the gravitational constant).
Its moment arm is proportional to the sine of the lean angle.
M * (V * V) / R * cos(Theta) = M * G * sin(Theta)
Divide both sides by M (it cancels out) and you get:
(V * V) / R * cos(Theta) = G * sin(Theta)
There are other factors like Mass, height of the center of gravity, etc.
But they are not shown here because they cancel each other out and thus do not affect the equations.
That doesn't mean they don't affect handling.
They can affect handling tremendously - obviously, a GSXR-750 handles better than a Harley Road King.
But they don't change the lean angle for a given speed and turn.
Of course, G is just a constant too.
There are only 3 variables here:
As the bike moves through the turn, both torques are equal.
V: the speed of the bike
R: the radius of the turn
Theta: the lean angle