Why is the zener voltage increasing with the load resistance in this circuit?
Technically, increasing the load impedance is decreasing the load, i.e., putting lower demands on the supply.  That said...

You can easily get a voltage higher than the Zener voltage by pushing more than the Zener current through them.  I figure you have about 34mA going through the zener; the older ones are usually spec'd at 20mA, and newer ones tend to be spec'd at 5-10mA.  More current, higher voltage.

Even higher current, you can make it blink...after it heats up enough, there's enough electrons in the conduction band to make it a short.  Of course, as a short, it doesn't dissipate much power, so it cools down...and so on, ad infinitum.