Eberwin III was the eldest son of Count Arnold II of Bentheim-Steinfurt and his wife, Walburga of Brederode-Neuenahr.

Eberwin's younger brother Arnold married Magdalena Sophia (1540–1586), daughter of Ernest I, Duke of Brunswick-Lüneburg.

The families even agreed in the marriage contract that if Eberwin III were to die young, his younger brother Arnold should marry Anna.

After Anna's father, Count Conrad of Tecklenburg-Schwerin, died, a dispute broke out between Eberwin III and his wife.

Anna herself accused him of spending too much on luxury items, such as precious horses, and a portrait of himself by Hermann tom Ring.