Please, read my comment to the question first.
Try this:
SELECT t1.PatientID, t2.Height, t1.MeasuredDate, t1.BirthDate, t2.Weight
FROM (
SELECT PatientID, BirthDate, MONTH(MeasuredDate), MAX(MeasuredDate) AS MeasuredDate
FROM PatiensTbl
GROUP BY PatientID, BirthDate, MONTH(MeasuredDate)
) AS t1 INNER JOIN PatiensTbl AS t2 ON t1.PatientId = t2.PatientId AND t1.MeasuredDate = t2.MeasuredDate