Is there a known or quantifiable correlation between capsaicin and its effect on the body's metabolism?
Capsaicin do affect your metabolism. It affects your Capsacin receptors ( scientifically TRPV1 receptors). These receptor starts calcium influx into various types of tissues. In endothelial cells because of this it mimics stress response (McCarty et al 2015). Quoting from McCarty et al, 


  Clinically, ingestion of capsaicin-or its less stable non-pungent analogue capsiate-has been shown to boost metabolic rate modestly. opical application of capsaicin via patch was found to increase exercise time to ischaemic threshold in patients with angina


Coming to your question, there are scientific studies which suggest that capsaicin helps in maintaining weight by limiting weight regain after weight loss. Not just this, capsaicin has also shown potential in treatment of obesity. However you should remember that it will required specific amount of dose (you can check details in papers I cited ) to help maintaining your weight. Do not eat pound of jalapenos a day :P