Answer
DNP reduces the cell's efficiency to produce ATP. This increases the energy demands of the cell (i.e. more glucose is needed to produce ATP). As the cell needs more glucose for producing energy, excess glucose will not be diverted to anabolic reactions that increase the body mass.
Work Step by Step
The cellular energy need is primarily fulfilled by the oxidation of glucose, which feeds into the TCA. Other catabolic reactions also feed their intermediates to the TCA. The TCA generates NADH, which is converted to ATP through the ETC. Reduced ATP levels activate enzymes involved in glycolysis. Hence, more glucose will be utilized, and gain in body mass would not occur.