Improving your balance on a horse is a life's long quest. And one of the skills to learn is ability to imperceptibly soften contact during any gait/movement at any time. This is absolutely vital test of balance or lack of such for the rider and for the horse as well.

Humans have a very strong reflex to grab with their hands when balance is compromised. The reflex is so strong and so inborn it is extremely hard to overcome. And truthfully I do not think we ever can get rid of it. This is why giving beginner riders reins is a huge mistake. Before they even have a chance to substitute the reflex with something else they have reins in their hands and every time balance is lost hands are used to restore it somewhat. Developing independent seat is a must and a first priority. The famous Spanish Riding School in Vienna lunges it's riders for 6 months before allowing them to have reins which produces such elegant riders. I think this is absolutely the best approach to learning how to ride. I wish I started that way.
The less rider is balanced the easier it is to fall into trap of slightly holding on to the reins and thinking that it is your horse who keeps the contact. Unfortunately, many riders taught to think that way. And riders end up riding with heavy contact, or even worse, leaning backwards against it. This is not lightness or beauty.
When rider has learned to stay in balance at all gaits and transitions she/he can keep contact and offer the horse a bit in a very quiet, steady but soft manner.Riders must lighten the contact on regular basis, especially, when things feel good and check themselves. If a rider uses reins for balance it will be immediately obvious. Rider will be thrown backwards or suddenly becomes unstable and bouncy in the saddle.
It should become a habit, riding no more than 10 seconds without checking yourself. The give is minuscule, imperceptible. It happens almost in place. Sometimes just a small lowering of the hands is enough to achieve the desired softening. It is like rebooting your computer. It cleans things up. It helps to get rid of tension that may develop in the shoulders and arms. It is extremely sympathetic toward the horse, helps keep positive energy and reinforces the trust.

The softening of the hands is not only a test for rider's balance. It is also a test for horse's balance as well. This softening will clearly show if a horse honestly stretching into the bit or simply leaning on it. If softening of the hand made horse move faster, lean heavier or change in any way it is a warning sign that the horse is not balanced enough on its own. The horse uses reins and the bit as a 5th leg and the rider unwittingly plays the game by holding back and struggling with too much load. A horse that properly stretching will not really need it for balance. It is a communication device not a balancing rod. A horse touches the bit to stay in contact with the rider and rider can assess the horse's physical and mental state by the quality of the contact. When rider feels the horse moves well and listens well she/he must soften contact to give the horse a chance to be on its own. It is a praise and a gesture of respect and trust.
It is said after every successful half-halt there should be a yielding of the hands. However, if half-halt is executed with predominance of the seat and reins are only a finishing touch the yielding happens on its own. Horse rebalances and stops leaning which makes contact softer and if rider is balanced properly she/he will not punish the horse by continuing pulling or holding. However, the more important softening happens when everything seems to go well. This is the one many riders forget to do. Lightness happens not when you have a constant number of pounds in your hands. Lightness happens when you have only the weight of reins and a feel of soft chewing, gentle touch of the horse's relaxed jaw to the bit.

Happy riding...