1.
If something eats into your time or your resources, it uses them, when they should be used for other things.
Responsibilities at home and work ~ his time...
PHRASAL VERB: V P n
2.
If a substance such as acid or rust eats into something, it destroys or damages its surface.
Ulcers occur when the stomach’s natural acids ~ the lining of the stomach.
PHRASAL VERB: V P n