Diet-induced obesity is becoming more common all over the world, which is increasing the prevalence of obesity-induced chronic diseases such as diabetes, coronary heart disease, cancer, and sleep apnea. Many experimental results show that obesity is often associated with an elevated concentration of plasma leptin and triglycerides. Triglycerides inhibit the passage of leptin across the blood–brain barrier (BBB) to signal the hypothalamus to suppress appetite. However, it is still not clear how triglyceride concentration affects leptin transport across the BBB and energy balance. In this paper, we propose a novel ordinary differential equations model describing the role of leptin in the regulation of adipose tissue mass. Analytical and numerical results are analyzed using biologically relevant parameter values. Additionally, we perform sensitivity analysis of the equilibria and study the sensitivity of triglyceride production on leptin resistance. Equilibria analysis and simulation results show that triglyceride production plays an important role in determining the fat mass in an individual. As weight increases, the occurrence of leptin resistance increases. Obesity enhances the likelihood of creating a vicious circle, where more fat mass leads to greater leptin resistance. Thus, control of the triglyceride production may be effective in reducing the occurrence of leptin resistance.