Obesity is a contributing factor to asthma severity; while it has long been understood that obesity is related to greater asthma burden, the mechanisms though which this occurs have not been fully elucidated. One common explanation is that obesity mechanically reduces lung volume through accumulation of adipose tissue external to the thoracic cavity. However, it has been recently demonstrated that there is substantial adipose tissue within the airway wall itself, and that the presence of adipose tissue within the airway wall is related to body mass index. This suggests the possibility of an additional mechanism by which obesity may worsen asthma, namely by altering the behaviour of the airways themselves. To this end, we modify Anafi & Wilson's classic model of the bistable terminal airway to incorporate adipose tissue within the airway wall in order to answer the question of how much adipose tissue would be required in order to drive substantive functional changes. This analysis suggests that adipose tissue within the airway wall on the order of 1%-2% of total airway cross-sectional area could be sufficient to drive meaningful changes, and further that these changes may interact with volume effects to magnify the overall burden.