Doing them both on the same day reduces the effectiveness of both. Best to just alternate days. Like, MWF do weights, TThSa do cardio. Use Sunday as a rest day.

Putting aside this “integrated nutrionists” opinion on which order is most effective for what, which appears to boil down to “no one knows, so here’s what I think,” alternating days is best. If you’re strictly trying to burn calories, you should do whatever form of exercise you can do longest. Walking, especially with varied terrain like hiking, burns a tremendous amount of calories. As my friend likes to say, it’s the miles covered that count, not how fast you do them. If you cover 10 miles of ground each day through daily activity and sustained exercise (yes, even just walking), which isn’t actually that hard, you’ll burn a lot of calories.

If you’re doing both weights and cardio in the same session, you should do weights first simply because being tired out from cardio before hitting weights increases injury risk.

Want to know what will make you gain weight and lose muscle most effectively? Injuring yourself.