When our horses are heavy in our hands, the first thing that pops into my head is that your horse is travelling on their front end, and not working off of their back end.
It could be your horses conformation, but it also could be you - not riding correctly, to aid your horse to move correctly.
Your seat is very important, to activate the back end, your legs are important to lift your horses ribs/spine up into your seat. Your upper body is important to remain over your horses center of gravity. Your shoulders are important to remain back to aid your upper body, your hand carraige is important to aid your horses front end to lift up and rock back.
All are important key factors to aid your horse in moving correctly. Without one, the others cannot be effective. You lose one, the domino effect occurs and all the others fall down.
You can do all the transitions you want, but they wont be effective if you, the rider, isn't being effective in the saddle.