A 22 gallon tank only holds about 6 gallons of water. At that depth and pressure, the 7G05 is trying to pump about 8 GPM. That means if you are using a 4 GPM shower or sprinkler, the other 4 GPM goes into the pressure tank for 1.5 minutes and the pump shuts off. Then the 4 GPM drains the tank in 1.5 minutes and the pump comes back on. That is a cycle every 3 minutes, which can be 480 cycles in a 24 hour period, or 120 cycles in a 6 hour sprinkler zone.
I am sure you are also noticing the pressure in the shower change from 40 to 60 and back again every couple of minutes, which can be irritating. A CSV1Z set at about 55 PSI will deliver constant pressure to the shower or sprinklers. The back pressure from the 7G05 will only be 130 PSI, so even 160# pipe is fine. Yes it should go in place of the above ground check valve. The CSV will increase the life of your pump system, and give you much better pressure in the shower.