I don't understand the formula for calories burned based on hear rate. According to it, a person with a lower weight, doing the same exercise for the same amount of time will burn LESS calories than someone with more weight. It sounds counterintuitive as you would assume that more energy would be required to move greater mass. Am I missing something from these formulas?
This has nothing to do with the formula based upon heart rate , it's the way it works even when you are not exercising. Every single part of your body from your organs to your muscles requires energy to survive. That is what your basal metabolic rate is based upon. The more of you there is, the more energy is necessary to keep you a float. When you are exerting yourself more than just existing like walking or standing even sitting you need to expend more energy to support that. The amount of energy necessary once again goes up if there is more of you. The formula of calculating calories based upon heart rate is simply a way of correlating hr to energy output (FYI it's not a highly accurate formula). So naturally the same principles will apply to the formula that it will assume your output is more if you weigh more
How many calories did I burn while doing [ACTIVITY]?
Unfortunately, any answer to this question can only be an estimate at best, and it is not wise to trust any number to be 100% accurate. However, there are a few reference lists that can be used as a rough estimate:
Note: Remember F=ma? (or Ek=0.5mv^2) you need to exert a force to do a activity which requires energy. The amount of force (and hence amount of energy required) is equal to the product of mass and acceleration. More mass that needs to be accelerated (bodyweight) the more force required and so the more energy used.