KVL not satisfied during simple diode series
It seems your voltmeter has an input resistance of 7.5M ohms, that would give the results you see.  

Each time you connect to the circuit you are placing that resistance in parallel with the component.  

So when measuring across the diode 1uA will flows and you see the voltage divider action.  

But when measuring across the 2.5M resistor the diode stops all current, so that is why you see 0v.  

Try modeling the equivalent circuit.  

(Credit to Photon as he hinted to this in the first comment).