Generally speaking, YES, it is better to do weights first.
Why on earth you would do both back to back is beyond me. As someone clearly pointed out, keep them seperate.
If you want, do your cardio first thing in the morning on a empty, or semi-empty stomach (NO MORE than 30 min and MODERATE!! LEVELS). Later in the afternoon do your weights (and make sure you eat well during the day before you do this too).
Just keep them fuckin seperate OK?
There are better explanations as to why but for simplicity's sake let's just say it like this. If you waste your energy on cardio before weights, you won't lift as much, and as well cause you've already spent a chunk of your energy on the cardio. If you're not pushing as much weight as you should because of this, you're sort of wasting your time lifting as it does not create effect that weights should have.
It's not entirely correct but think of it that way and you'll be fine.