It looks to me as if lots of people do weights and cardio on the same days. I never do that, unless you count a little jump rope between lifts to loosen up.
My reasoning is that a weights day calls for at least one (or two days for those over 40) of active muscle recovery, by which I mean just calisthenics or "cardio." That's why I have weights days, "cardio" days, and calisthenics days.
However, if you do cardio and some heavy weights on the same day, do the weights first. If you do them the other way around, you may not have the oomph to move the amount of weight you need to.