Acute malnutrition is manifested by –
Weight for height

This compares a child's height with the expected weight of a healthy child of the same height.
Combination of these measurements have been suggested sometimes to distinguish 'type' of malnutrition.
For example, water low proposed that weight/height allows one to distinguish between children who have suffered malnutrition in the past front those who are currently experiencing malnutrition.
In chronic malnutrition, the child is stunted i.e. his weight for age and height for age are low. Therefore, weight for height cannot diagnose chronic malnutrition as chronic malnutrition affects both weight gain (weight for age) and linear growth (height for age) → Weight deficit is proportionate to the deficit in height.
In acute malnutrition however his height for age is appropriate but he is wasted (low weight for height and age).
Thus weight and height measurements together are useful to understand the dynamics of malnutrition, distinguishing between current malnutrition and long-term or chronic malnutrition.
Wasting (deficit in weight for height) usually signifies acute onset malnutrition.
Stunting (deficit in height for age) usually signifies a chronic course of malnutrition.
Wasting and stunting → Acute on chronic malnutrition.
Underweight (low weight for age) → Combined indicator to reflect both acute and chronic malnutrition
Weight for age
Weight for height
Age for height
Brocas index