If you’re goal is to lose weight then doing cardio after your weight training is especially important. The simple reason is that weight training depletes glycogen is muscles. What is Glycogen? Glycogen is a primary a fuel source for cardiovascular exercise. When the glycogen depletes in your body it is more likely release fat from cells to be used as energy. When you do cardio without weight training before, it takes around 20-25 mins for glycogen levels to fall and fat cells to potentially be released. Here is a link discussing the role of carbs and glycogen for use in exercise.
You should save your maximum amount of energy for the weights. Lifting weights takes a lot of energy and it is important to use proper form to prevent injuries. If your body is already tired from running there is an increased risk that you won't use proper form. This also limits your potential for muscle building as you won’t be able to do as many reps that you otherwise could.
Here is a video I found on YouTube that talks about why you should weight train before doing cardio workouts