At DFW, it's almost always best to take the train if in a hurry. It is big enough that trying to walk or run between terminals is slower, even if they are all connected on foot.
The aircraft currently showing as operating the PHX-DFW in July are all mainline: A320 class or 737-800. I think these are not usually subject to weight restrictions even when it is hot on such a short flight. So unless AA change the route to American Eagle operators (which is not likely between now and then), you should be fine.