I briefly ran into this problem with my mare. It is so easy to develop hard hands on a horse that expects you to carry it, lol.
Are you heavy handed because your horse is heavy? If so, it will be beneficial to work on your horse at the same time. With my mare, we did tons of transitions. At the walk, ask your horse to woah by taking a deep breathe in. On your exhale, tighten your tummy muscles, close your fingers just enough to squeeze the reins, and sit deeeeeeep in the saddle. In my experience, 9 out of 10 horses will at least hesitate.
Give your horse a chance to show that he can be soft. Maybe you have it ingrained in your head that your horse isn't. Try asking for things super gently. Give him a chance to respond. Once you can see how little pressure your horse actually needs, it's easier to be more forgiving with your hands.
Essentially, I tried riding with just my seat. I had light contact, but really tried to work on controlling speed, tempo, bend, etc with my seat. All it took was for me to realize my horse could be soft as a butterfly to lighten up on her.
I hope that helps!