This 1981 study examines marijuana use and attitudes in the 10 states that had previously removed possible jail time as a penalty for simple possession of marijuana. As the abstract says, "the study attempted to assess the impact of the law on the attitudes, beliefs, and peer norms of high school seniors and young adults relating to marijuana use. ... Overall, the results indicate that decriminalization of marijuana had virtually no effect either on use or on related attitudes and beliefs about marijuana use among young people in this age group."
This report by Release.org, a British organization focused on harm reduction in drug policies, looked at data from over 20 countries that have adopted some form of decriminalization of drug possession, including several that have only decriminalized marijuana possession. It found that decriminalization did not lead to significant increases in drug use in those countries, strongly indicating that harsh penalties for possession have little to no effect on drug use rates.