Be more specific. Damage to your body? Damage to your home? To the environment? What kind of "damage"?
Floors in gyms that are used for weight training are generally rubberised. This is to prevent damage to the floor if a weight is dropped from a height.
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The broken wooden bed frame in the bedroom was caused by excessive weight or pressure applied to it, leading to structural damage.
Excessive stress to joints can cause joint inflammation and eventually cartilage damage.
For free weight training I would look in to http://www.sparkpeople.com/resource/fitness_articles.asp?id=1033. It is a very informative article that discusses the benefits of weight training and gives you tips on weight training.
weight training strengthens your skeletal muscels
Most of the damage caused by tornadoes is the result of extremely powerful winds.
It caused a lot of damage like destroying buildings
The damage to the wall was caused by a heavy object falling onto it.
It is damage caused by the sun.
Strength and possibly power (depending on the type of weight training)
Muscle training is lifting weights and weight exercises