Length is more the issue than weight. It just so happens that they kinda go hand in hand.
The reason why recommended twist rates do not always hold true(as Shynloco states) is that RPM is the actual determining factor of whether a bullet will stabilize or not. Twist rate just happens to be the simplest way the manufacturers can convey this information to the consumer, because most do not have a chronograph.
Recommended twist rates are "generalizations". In other words, they are what will work most of the time, in most rifles, chambered for a given caliber/cartridge, with a given bullet. At pressures which are known to be safe. They are not written in stone.
Higher velocity will often stabilize a bullet that is supposedly too long for a given twist rate. With higher velocity, however, comes higher pressures. Manufacturers do not want to go out on a limb and specify something that could possibly be unsafe in some rifles. Therefore, they stick to "generalizations" and what they know will be both safe, and workable.........