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> The wearable would see the increased heart rate when a person is moving with a heavy backpack versus moving without one.

I'm sure it would notice the heartrate was up, but how is it supposed to translate that into energy consumption? Eg, my heartrate is 80 bpm. How much energy am I burning in an hour? There isn't enough information to say, even if we add in data points like a gps measure of my velocity and elevation change.

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It's not super far fetched to come to approximation, conservation of energy and all that, the main variability people in energy expenditure comes from activity.

Get population averages of base metabolic rate based on sex/weight/age etc. Get base heart rate. When heart rate increases due to activity,estimate what activity and intensity and use weight to estimate activity expenditure on top of base. A lot of assumptions of course which make these tend to be inaccurate but if the assumptions are right then methodology is not that unsound.

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> I'm sure it would notice the heartrate was up, but how is it supposed to translate that into energy consumption?

Well, you need more oxygen to burn more nutrients. This means faster heart rate.

The body normally doesn't want to waste energy, so the heart rate at any given moment is just enough to cover the requirements.

Precisely calibrating that is another story. You can go into one of the places that directly measure the oxygen use and get the baseline data (e.g. https://www.dexafit.com/services/vo2-max-testing )

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