The obese gene (OB gene) secretes a protein that functions in the signaling pathway of adipose tissue and adipocytes (fat cells) produce the hormone leptin ([reference][1]). 

> When the amount of fat in the body increases, the amount of leptin
> released into the blood also increases and signals to the brain that
> the body has enough to eat ([reference][2]). Inversely, studies in rodents suggest 
>that a reduction in leptin level during weight loss signals to the brain 
>to increase feeding and decrease energy expenditure ([reference][3]).

Other molecules have a role to play in the ratio of BMI to leptin like the ghrelin hormone ([reference][4]). The genetic and environmental factors other than overall adiposity may also regulate leptin concentrations ([reference][5]) which is why individuals with the same weight may have different leptin concentrations. 

A study has reported finding a strong exponential relationship for leptin levels with body mass index (BMI) ([reference][6]). Hope that answers both your questions. 
 


  [1]: http://www.ncbi.nlm.nih.gov/pubmed/8717050
  [2]: http://www.ncbi.nlm.nih.gov/books/NBK22251/
  [3]: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2430504/
  [4]: https://en.wikipedia.org/wiki/Ghrelin
  [5]: http://europepmc.org/abstract/med/8910093
  [6]: http://press.endocrine.org/doi/abs/10.1210/jcem.82.9.4251