When I first heard of the anthropormorphic principle, I felt the same way; that it was not a good argument, but the more I heard non-simplistic versions of it, the stronger it got.
Here is some interesting comments from Wheeler, but he doesn't get into the specifics.
But it was new in the form that Dicke put it. He said if you want an observer around, you need life, and if you want life, you need heavy elements. To make heavy elements out of hydrogen, you need thermonuclear combustion. To have thermonuclear combustion, you need a time of cooking in a star of several billion years. In order to stretch out several billion years in its time dimension, the universe, according to general relativity, must be several billion years across in its space dimensions.
So why is the universe as big as it is? Because we're here!
Stronger than the anthropic principle is what I might call the participatory principle. According to it we could not even imagine a universe that did not somewhere and for some stretch of time contain observers because the very building materials of the universe are these acts of observer-participancy. You wouldn't have the stuff out of which to build the universe otherwise. This participatory principle takes for its foundation the absolutely central point of the quantum:
No elementary phenomenon is a phenomenon until it is an observed (or registered) phenomenon.
Cosmic Search Vol. 1, No. 4 - FORUM: John A. Wheeler
Imo, the participatory principle Wheeler is talking about mandates that no definite, single form of physical existence could occur without observation within the universe itself. It's complicated and perhaps a sort of Universal Observer principle is all that is needed, or perhaps Wheeler is correct, or perhaps something else is, but this is not a lightly dismissed area.
Quantum physics, imo, provides some real teeth to the anthropomorphic principle.