EDIT: I tested this idea in a simulation and it (un)fortunately failed.
This post is an attempt to combine some parts of frequentism with some parts of Bayesianism. Unfortunately, there is a good deal of probability theory. I assume that "improper priors" are okay to use and that we have no prior knowledge about the population of which we are trying to learn.
THEORY
Let's say we're trying to estimate some parameter, B. If we interpret the likelihood function as a conditional probability function, we get a function for our posterior probability density function after taking n samples:

This yields an expected value of B:

Now, intuitively, it would make a lot of sense if, given B=b,... (read 254 more words →)
Since this seems like a question at the center of this whole thing, I just wanted to double check using other sources. Using [this](https://www.omnicalculator.com/health/tdee) calculator with the "little/no exercise" setting, I see
Female; 36; 5'4"
Weight: 65.5 kg -> 78 kg
TDEE: 1596 -> 1746
Diff: 150 kcal/d
If we set it to "moderate exercise", the gap increases to 194 kcal/d
[This](https://www.niddk.nih.gov/bwp) calculator yields similar results
So, pretty much in line with your conclusion.