This aerator is fed from the well pump and holds water at atmospheric pressure right; meaning the aerator is not pressurized? Your shut off valve and then this check valve is on the outlet of the aerator tank right?
If so, you have flooded suction to the jet pump and the water level in the aerator tank is probably higher than the jet pump, right?
At the lowest water level in the aerator, if the pump inlet pipe is still lower your'e fine, if the water level is lower than the pump's inlet pipe, you need a foot valve in the aeartor on the end of the pump's suction line.
If the water level is always up to the pump's inlet height, remove the check valve and put it on the outlet of the pump before the pressure tank. The pump will keep prime as long as the water in the aeartor is as high as the pump's inlet pipe and the check valve on the outlet will prevent the pressure tank from bleeding back through the pump into the aerator causing cycling of the pump on/off.
I don't like a pressure tank to be plumbed on a tee before the tank inlet. I like to go past the tank, feeding the tank off the main line to the house. That way the water flow direction does not have to change direction when the pump comes on or goes off, which causes water hammer when it does like in your design.
I would not build or use any type of hammer arrestor, that treats the symptom rather than the cause and an air chamber type will allow the air to be absorbed into the water and that prevents it from working. Then you drain the water out of the system to get air back into the chamber; over and over'n over for ever.
You should set the air pressure in the pressure tank to 28 psi with no water in the tank and then adjust the switch to 30/50.
How do you control the water level in the aerator and the well pump?