CH1YO
Your first source hits on this even but you're considering height as a predisposition rather than a measurement. That's just wrong.
The sources quoted clearly use the word "influence."
An indicator is a marker. Indicators do not cause something to happen. They are the result of something.
For instance, doctors often check the blood for increased cardiac markers when they suspect heart injury. Raising cardiac markers does not increase heart injury; rather, heart injury causes a raise in cardiac markers. Thus, elevated cardiac markers are an indicator of heart injury.
Influences change how something happens. Influences are not a result of the change; rather, the change at least partially results from the influence.
For instance, doctors may give blood to reverse a low hemoglobin. They can predict that 1 unit of blood will increase the hemoglobin by about 1 point. A raise in hemoglobin does not cause blood to be given; rather, giving blood causes a raise in hemoglobin. Thus, a blood transfusion is an influence of hemoglobin, not an indicator.
A tall child does not cause a tall parent. Rather, a tall parent causes a tall child. So a parent's height influences a child's height, while a child's height indicates a parent's height.