Most homes have heavy furniture in them. They might seem stable, but that is when no one is climbing on them. Accidents happen when children view furniture as a playground and the furniture tips over.
To prevent this, you should install brackets to keep the furniture upright.
Usually, when you buy dressers and similar furniture, they come with these brackets in the box, but many chose to throw them out instead of using them.
If you do install a tip-over bracket, you should do so correctly, since a bracket that is not securely attached won’t do much good. Ideally it should be attached to a stud, since the drywall won’t have the strength to hold up a heavy piece of furniture. It should also be attached to a solid part of the piece of furniture.
If you have to use anchors instead, you will need to make sure they are rated for a large enough weight.