Three of these options clearly push metabolism up. An overactive thyroid floods the tissues with hormone that boosts oxygen use and heat output, so hyperthyroidism is a classic high $BMR$ state. Eating triggers the thermic effect of food, the energy cost of digesting and processing nutrients, which lifts expenditure for hours after a meal. Physical exercise obviously drives muscle metabolism and oxygen consumption upward. That leaves obesity as the only choice associated with a lower value, because the surplus tissue in obesity is mostly inert fat; once the rate is normalised to body weight or surface area, the obese individual reads relatively low. So the decreased basal metabolic rate among the options belongs to obesity.
\[\boxed{\text{Obesity}}\]