The present invention relates to a liquid milk fortifier composition for administration to infants, which fortifier composition comprises lipids in an amount of above 75 pcnt of the caloric content. The fortifier may be administrated to infants either as a supplement to human breast milk or to infant formulas. The present invention also relates to the use of the fortifier composition as well as a kit of parts for use in providing a lipid and/or calorie adapted body weight dependent nutrition to infants.