A directory of medical and recreational dispensaries in Mesa is listed below. If you need information on a specific store, click their profile link to learn more. The recreational purchase limit in Mesa is 1 ounce of flower or 5 grams of concentrate, and the medical purchase limit is 2.5 ounces. While medical patients from other states can possess up to 2.5 ounces of cannabis, they are not allowed to purchase medical marijuana at an Arizona dispensary, and must purchase from recreational dispensaries.