An eager appetite belongs to a family of sharp edges and sour tastes.
Latin acer included pointed sharpness. Its French descendants included sour or acidic taste, while English eager developed a familiar desire sense. Keenness links physical sensation and attitude.
These are selected senses; older languages also had figurative meanings. Intermediate Vulgar Latin and Middle English forms are omitted, and the senses did not replace one another neatly.
Sources
- Merriam-Webster: eager
Word History traces Middle English egre through French egre/aigre to Latin acer.
- Etymonline: eager
The entry gives Latin sharp/pointed senses, Old French sour/acidic senses and English keen desire, while recording overlapping meanings.