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It's obvious that as the weight comes off my HR should be lower for the same workout
Not really. The correlation between your heart rate and your performance is fairly weak.
In terms of weight loss and performance, all other things remaining equal*, if you are lighter, you are moving less weight around, so you'll be faster. This does assume that there's no functional loss associated with the weight loss.
* Not that they ever would be equal - It would be pretty difficult to disassociate weight loss from other physiological gains and functional gains, and if you are using running to lose weight, I would suggest that the torturous stats needed to separate the two would make the results meaningless noise.
tl;dr Skinny is faster than fatty.
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Your pace for the same HR is going to increase simply from the conditioning at that HR even if you lost zero kg - this is the principle behind the Maffetone Method.
To get a better idea, plug your current numbers into http://fellrnr.com/wiki/VDOT_Calculator and include your weight - it will give you predicted times if you lost Xkg. Enjoy your eating disorder!
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NotThamesWater
lamby
@Greenbank
Anyone got example (anec)data from losing weight and the effect it had on your running?
Right now I can run at a steady 10.5kph (5.40min/km) along the flat and my HR will sit around a comfortable 160bpm. This is me at ~88kg, I'm 5'8" so this is quite overweight. I'm on my way down to 76kg (and ideally 70kg but I will start with getting back to a BMI of 'Normal').
It's obvious that as the weight comes off my HR should be lower for the same workout (all other things being equal; weather, health, etc) but I know it's more likely that I'll end up running to the same perceived effort and going faster for the same or even slightly increased HR. (It doesn't get easier, you just get faster.)
I'm just looking for someone who's got HRM/GPS data from a time when they lost loads of weight who can say: "I used to do x min/km at y bpm and after losing z kg I can now do blah blah blah."