I was talking about moving the tweezers close to the terminals, not short them (which is pointless for a capacitance measurement).
I imagine you are zeroing it, but how stable is this zero value as you move around as you may during a measurement?
Not sure what the meter drifting represents. It uses AC, so charge should not be a factor. Capacitance is mostly a function of geometry (think the classical two parallel plates), which is why I was asking about the variation in open circuit reading. I imagine moisture in the air will affect the dielectric constant, so breathing on it may also very well change the value.
Can you reproduce the drift in open circuit reading if you just lay the tweezers on the bench without any movement or people nearby? Note that the meter is allowed to drift up to 0.02 pF for a zero reading, depending on the test frequency.