Preheat oven to 375°F. Spray a 8"x11" or two quart baking dish with cooking spray.
Cook onion in butter on medium heat until translucent, about 5 minutes. Add zucchini and cook for 4-5 more minutes to remove some water.
In a medium bowl, combine ½ of the stuffing mix, ½ of the cheddar cheese, eggs, milk, butter, and the zucchini mixture. Add just enough water for the stuffing mixture to be moist. Spread into baking dish.
In a small bowl, combine the remaining stuffing mixture, remaining cheeses and 3 Tablespoons of butter. Sprinkle over zucchini mixture.
Bake for approximately 25 minutes or until stuffing is lightly browned.