Horses that pull or brace on your hands, or that root, are looking for a release. Horses don't come braced, they get made that way by people. The horse that pulls and braces, and is heavy in your hands likely has learned this by being pulled on and never getting a release. The horse that roots has also likely been pulled on and has learned to get a temporary release through rooting.
The solution in all these cases is to teach the horse that there is a release to be found - a consistent, reliable, soft spot where everything's in balance and the contact is the merest whisper. But it's up to the rider to define and deliver that soft spot every time. When this happens, and the horse believes that the release is always there to find, all of the pulling, leaning, bracing and rooting behavior goes away, just like that. It's that simple.