Initially there are 2 ways to go
#1 Drop the contact. Horse "hanging" on hands, hands getting blisters? Make reins so loose horse can not depend on rider to hold their head up. When horse falls on face pick up reins and start riding normally. Repeat as necessary.
#2 Dropping contact hasn't worked - so what now? IF you are a GOOD rider and have CONSISTENT contact you can try this method - Keeping/maintaining same contact with outside rein - take inside rein and "bump" rein straight up in the sir then IMMEDIATELY revert that rein back to the original position. This means the horse, whose head was down leaning on the reins, will jerk head into the air and off your hands. Then horse will realize reins are back where they started and should go back to correct contact. Horse will not immediately realize the bump will be your method of training him/her to get off your hands - so you will need to repeat this MANY times in the future. IF rider is consistent with this correction (and performs correction correctly) then horse will eventually stop leaning so heavily on hands. If rider has no clue they will be introducing more problems to the horse. Clueless riders should stay with technique #1 (above). ALSO - horses need to develop the correct topline muscle in order to hold up their own head/necks, so fixing the problem permanently WILL take time.
Dressage is for Trainers!