I see people throw around the word balanced crank about single cylinder engines and removing the counter balancer. I kind of shake my head.
Your piston goes up and down. The crank is made heavier on the side opposite the pin in an effort to offset that. If you were to offset the weight equally (is that what you would consider balanced?), then you got rid of your vertical vibration and replaced it with a fore/aft vibration as the crank weight swings to the front and the rear. If you only offset half the weight and add a counter rotating shaft which also offsets half the weight, the crank and the counter balancer offset each other's fore/aft vibration. Often people want to remove the counter balancer to make the engine spin up faster. You'll get vertical vibration from the piston and rod not being fully compensated for as well as fore/aft vibration from the crank not being compensated for. It would be better from a vibration perspective to cut weight out of the crank and counter balancer and fill with a lighter material. Ideally, the weight would be removed equally from both sides and both parts to not affect the balance.