"Consume", "devour", "dwindle", and "erode" are some of the synonyms for the phrase "eat into". These words all imply a gradual reduction or depletion, whether it be physical or abstract. "Consume" can refer to the act of eating or drinking to satisfy hunger or thirst, but can also mean the gradual reduction or depletion of resources. "Devour" implies a fast or hungry consumption, while "dwindle" suggests a gradual decrease or wearing away. "Erode" refers to the gradual wearing away of a physical object, but can also be used to describe a slow but steady decline over time. Overall, these synonyms all evoke a sense of gradual transformation or loss over time.