So 620 miles a week is 1800 or so miles a month. Burning a quart in 1800 miles really isn't terrible. Check, and top up the oil weekly and it'll be fine.
Check for leaks, look all around where the heads meet the block for head gasket leaks. Pull the spark plug boots to see if oil is leaking through the plug seals, check if the valve cover gaskets are leaking, and check around the timing covers to see if the cam/crank seals are leaking.
Switching to a synthetic can increase oil leaks/burning on higher mileage engines. but you don't have a whole lot on that one. You may want to switch to a good synthetic just to increase your oil change interval to around 5k miles so you're not changing it all the time with all that driving.