Regardless of the bullet proper's weight, length, or internal composition, the barrel determines how fast a bullet twists in flight. How does its weight affect how the copper or outer layers break up from spinning?
The barrel determines how far the bullet has to travel in order to spin around once. The forward speed of the bullet determines how much time it takes to travel that distance.
The faster the forward speed, the less time it takes to spin once or the faster it is spinning.
The faster something spins, the larger the force that acts radially out from the axis of the barrel (or the axis of the spin)(the centrifugal force if memory serves). It's that force that tends to make the bullet come apart.
So, to answer your question about weight, the less the bullet weighs the faster it is going to move forward (assuming the powder charge stays the same), the faster it spins and the more the centrifugal force is.
The main point is that it isn't how far the bullet has to travel to spin a certain angle that determines the centrifugal force, it's how long it takes to spin through that angle.
As to whether the bullet comes apart or not under this force, that has more to do with how it is constructed.