Obesity is a physical state i.e. someone has a bmi over 30, or weighs over a certain amount compared to their weight. It could be a symptom of a disorder/disease, but in itself is not a disease.
Because obesity is not a disease, it cannot be the same disease as anorexia (AN). Obesity is extreme, yes but it is not the opposite of AN as some like to think. The physical state that is the opposite of obesity is emaciation.
An ED that could cause obesity is compulsive over eating disorder (COE) or binge eating disorder (BED). So, some people might see these EDs as being the opposite of AN, but they are not and as you say they are extremes. All EDs are extremes but AN and COE are really not that different. EDs all have similar causes and AN, BN, COE etc are all linked closely. In fact many EDed people are not strictly one disorder, they show a combination of ED behaviours/symptoms.
Also, do not assume that all AN sufferers are emaciated.
Meh, whatever. All EDs are misery.