Do hangovers get worse with age? Why?  

Brain Changes. The more alcohol you take in, and the longer you drink, the more changes occur to the brain, and the chemistry of the brain. Withdrawl is worse with age, hangovers are worse, dying from withdrawal is more likely. Treatment programs offer medication to make withdrawal safer, proper nutrition, vitamins and minerals that help the brain to recover, and support to prevent relapsing to alcohol.
Hang over. Generally people tend to drink more when they drink , as they get older. The more alcohol the more side effects e.g. Dehydration and lack of good nutrition. Many people are not as healthy as they age, so they are less tolerant of abuses to the body like excess alcohol.