Orthodontics: Do braces weaken the teeth roots?
Orthodontic tooth movement does not weaken the roots of your teeth.
In a small percentage of people, a process called apical root resorption can occur where cells in the body resorb tooth roots making them shorter. This is part of the informed consent. Your orthodontist will take radiographs during treatment to monitor for this among other things.
It is not necessarily something that can be predicted or prevented just yet. Fortunately, bad cases are rare, and even if the root resorption is pretty severe long-term studies have shown that the teeth still hold up well.