I often times ponder this. I'm 220 right now. 5'11". Yes this qualifies me as obese. It is fat too, not muscle.
Consider that last year, at 222 or 223 pounds, I ran 1:40:03 in a half. It was a pretty good effort for me.
Now consider that two years prior, at 195 pounds, I ran 1:26:20 for a half.
My volume of running was similar, my intensity of training paces was similar. Of course my actual paces were slower due to the weight, and I did age two years, but I'll exclude that as a factor.
That means that gaining 27 pounds (195 to 222) cost me 13.5 minutes. Pace for the 1:40 was 7:37, pace for the 1:26:20 was 6:35, or 1:02 per mile.
That's 2.3 seconds per mile. Now I'm sure my training intensities were not exactly the same, and yea maybe going from age 38 to 40 has some effect too. But no doubt the biggest variable was weight gain.
It seems completely reasonable to me that if you have non functional weight to lose (fat), then something like 2s/mi is reasonable.
Now if I lost a ton of weight to put me in the middle of my normal BMI, say 160 pounds, would I really be able to linearly scale my improvement? I seriously doubt it. No way I'd be running a 1:13 half.