I just the same test with a 1:1 probe and the waveform is still the same between 2 and 4V. So I can eliminate that the probe the culprit, as have correctly predicted by Ron H.
For what it's worth I start my test by connecting the DMM. I then add the scope or remove the DMM and chech with the scope. I've not noticed any shift but that doesn't mean it isn't happening.
What I will do though is to use the 10:1 probe just to see what happens.
Thanks for working thru this with me. It's supposed to rain tomorrow -perfect day to tinker a bit on the bench for a bit.
When you measure frequency, do it on pin 3. Then you won't be changing the capacitance or resistance of the timing circuit.
Maybe the cap on pin 5 is leaky. You can safely remove it. I don't think that's the problem, though. It would also affect the upper threshold, and even more so than the lower one.
For what it's worth, I built several versions of this with different parts. Admittedly the capacitors at pin 5 came from the same batch of older disc capacitors. It's certainly possible that they've deteriorated. Easy enough to remove!