So I misspoke earlier. Hioki is correct: Z = Rs + iXc, Where Rs=ESR. So I answered my own question, but I had to go back to my texts to refresh my 67yo memory.
Xc is the capacitive reactance and: Xc = 1/(2*Pi*f*C). So, as frequency goes up, the reactance gets smaller, and as frequency goes down Xc gets larger.
ESR specifications are done at a frequency where Xc is very small compared to Rs (ESR). So basically where Z is essentially equal to Rs.
Your are quite correct in that capacitance readings are better at lower frequencies for the inverse reason. At sufficiently lower frequencies Rs is very small compared to Xc, such that there is little contribution to the determination of C from Rs.
So, why not use 1MHz to determine ESR? Good question. As frequencies rise other factors become more dominant. For example, series inductance becomes more and more of a factor as the frequency rises and at some point it will dominate all the other measurements.
BTW, those tweezers are doing a phenomenal job. If you do the math, both the reading at 10kHz and at 1kHz make perfect sense.
BTBTW: Given the above and looking at your results from the IM3570. We have @100kHz ESR=19.29mOhm and @4Hz we can calculate Xc @ 39.8ohm, so the Z measurement of 41.8 is not very far off at all.