She was always too small for her breed. Not sure why she was sick.

Sounds like a runt, which is fairly common with cats and dogs. That’s where “the runt of the litter” came from. It also applies to farm animals with singles litters (cows) and larger litters (pigs). I have not seen it get applied to a bird before, but it make sense.

A runt is just something with a low birth rate. It turns out that there’s a very strong correlation between birth weight and health.