I've heard this natural weight stuff before, but I know in my experience that my "natural weight" is more just the spot my body wants to plateau at, and once I get past the plateau my "natural weight" changes.
For instance, for ages I thought my natural weight was 132. It seemed that no matter what I did, my weight would stay at 132. I could like 4-5 lbs, or gain 4-5 lbs, but after a few weeks my weight would settle back at 132. I stayed at 132 for nearly a year and was resigned to believing it was my "natural weight".
I finally did break through that plateau by lowering my carbs, and upping my workouts, and now my "natural weight" seems to be stuck between 127-124. I have been in this weight range for the past 3 months or so, despite keeping up a fairly consistent routine.
about 3 years ago, I was consistently staying between 116-120... I was there for about 6-8 months without even trying and only gained when my medication was changed.
I guess what I am trying to say is that there may be ideal weights for certain heights/body types, and age, medication, etc. come into play, (for instance, I will never be able to healthily maintain a weight below 110, nor can I healthily be at 145) but I don't believe that there is such thing as a narrowly defined "natural weight". There may be a weight span that is easy for you to healthily maintain, but adjustments to your diet/activity level are likely to change that weight-span.