The ideal body weight for 165 cm height is between:
50.37 kg - 68.04 kg (metric)
111.04 lb - 149.99 lb (imperial)
Reference: BMI classification
Your body weight is in the normal range if your BMI is between 18.50 and 24.99. Using these values and your height in the BMI formula, we can find the lower and upper range of body weight that is considered healthy.
BMI = Weight/ (Height * Height), where weight is in kg and height in meters.
Since BMI value is independent of sex, the following weight range is applicable for both adult male and female who are 165 cm tall.
Lower bound: 18.5×1.65×1.65 = 50.37 kg
Upper bound: 24.99×1.65×1.65 = 68.04 kg