Why was Darwin's Finch argument valid considering Weismann's argument?
Weismann's mouse tail experiment showed that mouse tail length is not inherited, if the change in tail length was caused by mutilations, and there was an absence of selection pressure. 

However, Darwin's finches represented a completely different idea of evolution. In this case, the beak size of the finches did in fact change, but this was not due to mutilation. The beak sizes of the finches changed because finches with lower fitness due to their beak sizes were selected against, leading to the beak size changing over time. 

If the mice were instead selected for tail length by preventing the long-tailed mice from reproducing, then it is indeed possible that the mice would eventually evolve to have shorter tails, or even absent tails. 

Similarly, if the finches had their beak sizes reduced artificially but their fitness preserved (for example, by grinding down their beaks and feeding them soft food that does not require large beaks to break), the finches would not be expected to evolve smaller beaks. 

It is not clear which method is the one through which the evolution of the overbite occurred. It could be due to a change in relative fitness, but a case can also be made in which fitness was not a large factor.