I overheard this once, but can't seem to find the origin of this quote. I checked Bartlet, Times, Yale, and Oxford, so I'm positive I heard it wrong. It might have been "the taller the tree." I am familiar with "the taller the tree, the deeper the roots," but in this context it was referred to as falling deeper into sin: The more potential a person has for greatness also makes one susceptible to fall even further. No idea where they got this from.
I believe this is a variation of an old German idea. The old nostrum is that The apple does not fall far from the tree. Meaning that a child usually has a similar character or similar qualities to his or her parents:
It was Richard Jente (1888-1952) who said it, or spoke of it in 1933 as an already old idea. [yahoo.com]
Sigmund Freud added the important detail of an apple; "Nor from the horse."