Many antique dressers have some damage to the drawers. This dresser was no different.
If there is too much weight in a drawer the bottom will push down and if your dresser has
metal drawer stops they will start to dig a groove into the wood.
The groove can get very deep, even go right through making a nice big hole in your drawer bottom.
To fix the problem move the metal drawer stop. You can pull it out with a pair of
pliers and use a hammer to re-install it. The bottom is a point that hammers into the wood.
If you don't have any drawers stops and you are looking replace them check out this article: