If you wear someone down, you make them gradually weaker or less determined until they eventually do what you want. They hoped the waiting and the uncertainty would wear down my resistance He believed that he could wear her down if he only asked often enough
If you wear something down or if it wears down, it becomes flatter or smoother as a result of constantly rubbing against something else. Pipe smokers sometimes wear down the tips of their teeth where they grip their pipes The machines start to wear down, they don't make as many nuts and bolts as they used to Elephants wear the tusk down faster than they can grow it