Genetic short stature and familial obesity: This is a common scenario where the child's short stature and overweight status could be attributed to familial tendencies, with the small head size being a normal variant or part of the genetic predisposition.

Hypothyroidism: Can cause growth delays, weight gain, and potentially affect head growth, though this would be less common.
Cushing's syndrome: A rare endocrine disorder that can cause weight gain, short stature, and potentially affect head size due to the effects of excessive cortisol.
Prader-Willi syndrome: Characterized by short stature, obesity, and often a small head size, along with developmental delays and hyperphagia.

Craniopharyngioma: A brain tumor that can affect growth hormone production, leading to short stature and obesity, and can also increase intracranial pressure, potentially affecting head size.
Pituitary gland abnormalities: Defects or tumors in the pituitary gland can lead to hormonal imbalances affecting growth and weight.
Chronic illnesses (e.g., renal failure, cardiac disease): Certain chronic conditions can lead to growth failure and weight issues, though these might be less directly linked to head size.

Noonan syndrome: A genetic disorder that can cause short stature, variable effects on weight, and occasionally a small head size, along with characteristic facial features and heart defects.
Russell-Silver syndrome: Characterized by growth restriction, small head size, and variable effects on weight, often with asymmetrical features.
Other genetic syndromes: There are numerous genetic syndromes that can present with short stature, obesity, and small head size, each with its unique set of features and complications.