The main weakness in my application was my weak research experience in the field I applied to. Say I got two new writing samples and greatly improved my research experience. Would it be acceptable for me to reapply to a school I got rejected from? I really want to go to that program.
I would reapply if you feel you have a better chance. It's definitely worth checking with the university to find out their admission policies for re-applicants. For example, I know of a university in the UK that automatically reject re-applications from candidates without even considering their CV or interview. Doesn't make much sense to me.