Should the authorities intervene in this situation?

Yes, the mother has clearly lost control of her child's eating and needs guidance otherwise it may get even worse.

Something needs to be done to help the child, but it's possible that the local authorities should simply monitor the boy's progress, rather than intervene directly.

No, local authorities will only confuse the situation even more. It's up to the boy's mother to make sure that the boy eats healthily. Local authorities can't help with that.