Why does my microwave trip my AFCI only when it's mostly empty?
Most microwave ovens will generate arcs and sparks inside their cavity if they are run with an insufficient load, or no load whatsoever.  The high-frequency content from these arcs is being coupled (likely capacitively) through the HV transformer section of your microwave onto the AC line, where the AFCI can then see it and proceed to freak out, thinking the arcing is actually an AC mains arc, not a microwave cavity arc.

Suggestion: throw a coffee mug of water in with the slice of pizza.  This does the same thing as Keshlam's sacrificial bread slice -- i.e. provides more load to absorb the microwaves instead of letting them bounce around the cavity until they arc, just without having to waste a slice of bread.