**Core Concept:** The presented symptoms are indicative of a hormonal imbalance or thyroid dysfunction, which can lead to weight gain, irregular menstrual cycles, and high blood pressure. These symptoms are often seen in conditions like polycystic ovary syndrome (PCOS), Cushing's syndrome, or hyperthyroidism.

**Why the Correct Answer is Right:**

Among the given options, Cushing's syndrome is the most fitting diagnosis for the presented symptoms. Cushing's syndrome is a condition caused by prolonged exposure to high levels of cortisol, a glucocorticoid hormone, usually due to an adrenal gland tumor or long-term corticosteroid use. The triad of symptoms includes weight gain (often central obesity with sparing of facial features), hypertension, and moon face or buffalo hump. These symptoms align with the patient's weight gain, elevated blood pressure, and oligo/amenorrhea.

**Why Each Wrong Option is Incorrect:**

A. Thyroid function tests (TFTs) are useful in diagnosing hypothyroidism, not hyperthyroidism. The patient exhibits hyperthyroidism symptoms (weight gain, hypertension, and irregular menstrual cycles).

B. Alkaline phosphatase test is indicative of liver disease or bony abnormalities, not Cushing's syndrome. The patient demonstrates Cushing's syndrome symptoms.

D. Random cortisol test evaluates the cortisol level at a specific time point and may not necessarily reflect the elevated cortisol levels seen in Cushing's syndrome. The patient exhibits Cushing's syndrome symptoms.

**Clinical Pearl:**

When assessing patients with hypertension, weight gain, and irregular menstrual periods, consider Cushing's syndrome in the differential diagnosis. A thorough medical history, physical examination, and appropriate laboratory tests (e.g., cortisol 24-hour urine free cortisol or dexamethasone suppression test) are crucial to confirm the diagnosis and initiate proper management.