With a properly working well, the check valve in or directly above the pump maintains the pressure in the line between the pump and the tank. There is no reason for a check valve at the tank, and it could be masking the problem. If there is a leak in the well, the pressure in the house will bleed off, but only if there is not an above ground check valve.
Have you actually watched and listened down the well bore while the pump is running? If there is a leak it can often be heard or seen in the well.
Pump sizing is not proportional to the size of the pressure tank. One can have a 500 gallon tank or a 20 gallon tank, the only difference is how long the pump runs between cycles. The purpose of a larger tank is to increase run-time and decrease cycling. As long as the well has enough water, the pump is designed to pump non-stop.
I am also wondering if you moved the switch when you moved the tank? The switch will not perform well unless is it at the tank.