As is always the case :-) I agree with Peachey and FDMaxey. But you should know that the two terms do not just apply to physical weights. You can use them, for example, to describe moods or environements. Amy tries to keep her emotions balanced. Amy's great joy was counterbalanced by the immense sadness of her parents sudden death. Between work and relaxation, Amy has a life in balance. Amy's job is highly stressful and demanding, yet she counterbalances this with weekends devoted to simple, quiet activities. Amy's love of Heavy Metal music is amazingly counterbalanced by her devotion to Classical music.

If I stack blocks on top of each other and the blocks do not fall down, the stack has balance. If I am carrying a plate of food in a restaurant, I am balancing the tray. If I am walking and not falling down, I am keeping my balance. Counterbalance involves two separate weights - one balancing the other. If you look up the word "trebuchet", which is a counterbalanced catapult, you will see one example. A weight scale where you have two trays, one with weights on one tray balancing some object on the other side, involves counterbalance. Simply put, counterbalance is a balance involving two or more separate weights, one counteracting the other. A balance can refer to any object or number of objects that have some sort of steady state and are not falling over.

The "counter-" part signifies "against". So when you counterbalance something (or use a counterbalance), you are using a weight, against another weight, to achieve balance.