The very truth is that there is no unequivocal answer to this question.I would say that it depends on the existing conditions.
1. First approach:weights first and cardio after
If cardio is going to be of high intensity-HIIT just to mention one case-it would be preferable to follow the weight session.High intensity cardio might perfectly sap our energy,strength and stamina and prevent us from an effective weight training workout.
So if our ultimate objective is muscular strength or hypertrophy we had better complete the weight session first.
If on the other hand we speak for a moderate intensity cardio session, I don't see any serious contra-indications to do it first.Such a session will burn no more than 20-25% of our stored glycogen which means that it will leave our body with enough supplies to carry out the weight session with dignity.
About the fat-burning dimension:the truth is that the anaerobic weight training workout will burn some glycogen and turn the switch a little more towards the fat burning mode.
But we should not miss the forest for the trees!!
2. Second approach :cardio first and weights after
If the main target is maximum fat loss then we definitely need an effective cardio session to burn as many calories as possible.Could you imagine running after heavy squating?Barely!
In this case our interest is to finish first with our demanding cardio and then continue with the weights -with the remaining stamina of course!
If the possibility of eventual catabolism is worrying you,you can face it with the proper duration and intensity of the cardio as well as with the right nutrition frame before,during and after the session.
Conclusion: act according to your mood and objectives.Don't forget that we should get the big picture and don't bother with the minutiae!!