Puzzled by voltage readings of a simple resistor network
in the values you are giving wiring resistance is ignorable.
in other words the voltage along wires is all the same for a single wire regardless where you tap it with the probing ends of your measurement device.
having said this the measurement points of the ends for R2 are the same as for R3.
you already got the Kirchoffs rule's right: at the joints the current splits (into two equal halves because the resistors are of same size and their other ends are bound together).
the system is simple here: R1 to R2-in-paralle-to-R3 means a 2:1 divider.
5V / 3 * 1 = 1,66V
5V / 3 * 2 = 3,33V

(as you already indicated: your breadboard setup might have had an error when trying to replicate the plan.)