Top-load washers with an agitator (late 2015 and newer) are designed to be slightly loose. This "wobble" allows the agitator to flex with the clothes when washing heavy loads, which helps protect clothing. The agitator does not need to be tightened; this is normal.
How do you fix a loose agitator in a washing machine?
https://www.youtube.com/watch?v=HdcdnMehCys
How do I fix the agitator on my GE washer?
https://www.youtube.com/watch?v=Qr4GzTJBho0&vl=en
How do I know if my washing machine agitator is broken?
The agitator should start to oscillate back and forth, mixing up the clothes in the water. If the agitator does not move, double check that the sensor is depressed. If it still does not move with the sensor depressed, the agitator is broken and should be repaired.
Why does agitator keep coming off?
The agitator could come off the base if not seated properly. It can easily be snapped back in place: Line up the grooves in the agitator auger with the agitator base. Turn counter-clockwise until it locks into place.
How do I know if my washing machine agitator is bad?
When the top half of the agitator in a top-load washer doesn't agitate as it should, or if you can turn the agitator back and forth freely, it could mean the agitator dogs are worn out.
How do you know if your agitator is bad?
The best way to tell if the agitator dogs are bad is to try to turn the top of the agitator. If the agitator will turn freely both ways, the dogs are bad and need replacing. If it only turns one way, the dogs are working properly and your problem is elsewhere.