The use of "among them being" is not strongly connected to the use of an infinitive, even though the infinitive happens to follow it. To see this better, you can separately replace "among them being" and "to moisten" and see that the meaning remains intact.
The original sentence is:
The eyes produce tears for a number of reasons, among them being to
moisten the eyes, to protect them from substances...
The sentence could be rephrased to retain "among them being" but use "the fact that" to avoid using the infinitive form of the verbs:
The eyes produce tears for a number of reasons, among them being the fact that they
moisten the eyes, the fact that they protect them from substances...
Another equivalent, which removes "among them being", but retains the infinitive, would be this:
The eyes produce tears for a number of reasons. One is to moisten the eyes.
Another is to protect them from substances...
Another equivalent, though not as good, would be this:
The eyes produce tears for a number of reasons. One is moistening the eyes.
Another is protecting them from substances...
This interchangeability illustrates that the "being" and the infinitive are not closely linked.