It is not a MUST that one must do both aerobic and weights on the same day. That's erronous thinking. However, you should be doing both aerobic activity and weight training and incorporating full body weight training, not just select muscles.
Having said that, it is better to start with weight training, then move to aerobic training. If anything, you can fatigue your muscles too easily with aerobic training, so better to do your resistance training first, then follow it up with your aerobic training.
It's also been hypothesized and proven in some exercise physiology studies that the lactic acid accumulated from aerobic exercise can serve to increase your endurance because lactic acid accumulated from the anaerobic weight training will then combine with the oxygen from your aerobic exercise, which means you continue to produce even more ATP for energy, which means you can go longer and stay stronger.
Bottom line- do weights, then aerobics. And as long as you're getting in a full body workout two times per week (or however you split it up), you're doing pretty good.
Koffee