Always make sure that if your horse is leaning on you, you use lots of leg, don't be afraid to be quite strong with them - short, sharp, strong nudges, while raising your hands slightly to help him come up. If the horse is using you to balance himself, he is probably not going forwards properly from behind and finds it quite hard to balance. Remeber he's only young and will probably improve with age. Go slow with him and keep him on larger circles and don't expect too much of him. Does he lean right from the very beginning of the ride or just towards the end? If the latter, he's probably tired.
Keep trying, he'll get it eventually, and when he does, it'll be amazing!
Fiona.
P.S I wouldn't recommend putting side reins on something so young, you would be better encouraging him to go forwards correctly instead of using artificial aids to correct a problem so early in his training. He could learn to rely on them and could be even worse when he finds himself without them.