This is a very common question that people ask when they decide to fit a cardio and weight workout into the same session. I’ve often wondered this myself and agreed to the consensus opinion on this matter: weights first. A cardio workout’s goal is for heart-rate optimalization so it’s ok to perform when you have fatigued from weight training. However, if you do cardio first, your muscles get fatigued as well so it will hinder your weight workout. I usually time my workouts so that they are from 45 to 60 minutes so I only do weights or cardio but rarely both in the same day.
Whatever you decide to do, just don’t mimic this guy: