Equivalent impedance calculations from "both sides"
I'm not sure why you care about the load impedance of the DAC inputs. The whole idea of an R-2R DAC is that the VA, VB, VC, etc. inputs must be voltage sources &mdash; i.e., essentially zero output impedance, or at least much smaller than the value of 2R.

If your "counter" does not have sufficient drive capability to meet this requirement on its own, you'll have to add a set of buffers to its outputs.

On the other hand, if the output impedance of the counter is consistent from bit to bit and between high and low, then you can simply reduce the value of your 2R resistors by that amount in order to take that into account.