First of all, the SAE levels are a convenient way of measuring how self-driving a car is and exactly what it can and cannot do. So the levels give us very useful information about the capabilities of the car.
In simple terms, the levels are:
Not self-driving:
Level 1: The car can perform steering OR acceleration/braking but the driver must supervise and monitor the environment
Level 2: The car can perform steering AND acceleration/braking but the driver must supervise and monitor the environment.
Self-driving:
Level 3: In certain conditions and environments, the car can perform all steering and acceleration/braking, can also monitor the environment but the car may request the "driver" intervene in certain situations where it might fail. The "driver" only needs to intervene when the car asks them to.
Level 4: In certain driving conditions and environments, the car can perform all steering and acceleration/braking, can also monitor the environment and can also intervene itself in cases where it will fail. The "driver" does not need to do anything at all when the car is in self-driving mode.
Level 5: the car can perform all steering and acceleration/braking, can also monitor the environment and can intervene in cases where it might fail in all conditions and environments. The "driver" never has to do anything at all.
Source:
Defining Self-Driving Cars and Automated Vehicle Systems in SAE J 3016 - ANSI Blog
Full self-driving by definition means that you don't need to pay attention at all. So if you do need to pay attention, then it is not true self-driving. And if you are using a weight on the wheel, you are merely tricking the system into thinking that you are paying attention when in reality, you might not be. Fooling the system so that it does not nag you to hold the wheel, does not make the system full self-driving either.
Lastly, the ability of a car to drive from A to B without driver intervention, does not in itself necessarily make a car self-driving. That is actually a common misconception that many people have about self-driving cars.
What actually distinguishes a self-driving car from a non self-driving car is how much the car can monitor the environment and respond accordingly. For example, can the car track and avoid collisions with other objects such other vehicles or pedestrians, respond to traffic lights, traffic signs, etc... That's because it is one thing to automate driving where the car can steer and brake to get you from A to B, it is quite another to do it safely. In other words, it is pointless for a car to be able to drive from A to B if it can't keep its human passengers safe. True self-driving is when the car can get you from A to B safely and reliably every time such that you know you could read a book or watch a movie and you would be safe.