What does "kill with kindness" mean?

Overwhelm or harm someone with mistaken or excessive benevolence. For example, Aunt Mary constantly sends Jane chocolates and cake and other goodies, even though she's been told Jane's on a diet—nothing like killing with kindness. This expression originated as kill with kindness as fond apes do their young (presumably crushing them to death in a hug) and was a proverb by the mid-1500s.