Step 1: Putting together unwanted coarse hair, irregular or absent menses and weight gain in a young woman points strongly to a single common endocrine disorder of the ovary.
Step 2: That disorder is polycystic ovarian disease, driven by raised androgens and failure to ovulate, frequently accompanied by insulin resistance, which neatly explains the whole symptom cluster.
Step 3: A hormone producing ovarian tumour would behave aggressively with fast virilisation and very high androgen levels, not the chronic, gradual pattern described here.
Step 4: Androgen insensitivity gives a hairless phenotypically female body in a 46,XY person, and Turner syndrome presents with short stature and streak gonads, so neither matches a hirsute obese woman with amenorrhoea.
\[\boxed{\text{PCOD}}\]