I'm really confused by the different depictions in media. They are usually shown to be very lean and wiry. Not particularly tall, sometimes even small.
This is the sort of question that is so entirely broad I won't be able to answer it properly.
However, as a Cherokee Nation citizen I'll do my best to answer your question regarding Cherokees, specifically.
Imagine a lacrosse player. Now imagine that lacrosse player was responsible for a lacrosse match that determined which tribe gained the hunting rights to hundreds of thousands of acres of land. How fit do you think he would be?
Stakes were extremely high among eastern woodlands tribes like Cherokees and Muscogee (Creek) for deerskins, which were constantly being traded with Europeans for metal goods and weaponry. Cherokees and Creeks, if not already at war, would settle disputes and secure hunting rights with the "little brother of war," stickball, which is still played today in the capital of Cherokee Nation, Tahlequah, Okla.
See also: http://www.cherokeeheritage.org/?page_id=237
Among Cherokees today, you can see all sorts of bodies. There are cowboys like Ryan Dirteater who fit the wiry type you mention, as do many professional bull riders. There are heavyweight boxers like Wes Nofire. (As far as women are concerned, I'd post a picture of my half-Creek Indian girlfriend but I doubt she'd be appreciative.)
Body types are as diverse in Indian Country as anywhere else, and probably at least as diverse as our linguistic variations, where you'll find more languages than in the entirety of Europe.
For the time period people largely study for Cherokees, we are often depicted as wiry, but that had more to do with our forced removal (Trail of Tears), loss of valuable land, internecine conflicts, and frontier life in Oklahoma/Indian Territory. Ned Christie, Cherokee statesman, is an awesome historical figure to study and certainly fits that wiry description.
http://www.cherokee.org/AboutTheNation/History/Biographies/NedChristie.aspx