A Columbia University research on the data of 1.7 million patients in a New York hospital shows that 55 diseases are associated with birth month. Averaged on all the diseases, people born in October and November have the highest risk and those born in May have the lowest.
Breaking down to specific diseases: Born in March you have a higher risk of nine types of heart disease. Born in December, higher in reproductive diseases. Born in November, higher in respiratory and neurological diseases. See the bar graphs in the Washington Post article.
But the strength of correlation with birth month varies too. See the circle at the bottom of the Columbia University article where the distance of the dot from the center represents the strength of correlation. Thus, acute bronchiolitis is very strongly associated with a birth at the end of November, viral infection strongly associated with a birth in mid-November, ADHD somewhat associated with a birth at the beginning of November, and hypertension rather weakly with a birth month in mid-January.