You might need to be a little more hard on this horse (not like mean) like when you turn or back up pull a little harder.

Unless he/she is a old schooling horse, is he/she green?

Did your trainer give you this horse to ride? If so, what does she say? Horses feel heavy in your hand because (from least degree of training to most)1.They are ignoring the bit and doing whatever they want 2. They lean on the bit and expect you to carry all the weight of their head and neck 3. They are used to going "on the bit" and expect a strong contact from their rider. Horses normally progress in their training through all these stages, so your horse could be in between two of these stages.
If 1, try to maintain a light contact with your hand, steer with a direct rein (like pull your horse's head to the side in the direction you want him to go) and give strong aids with your legs, make them the dominnt aids for him to listen to. If 2, maintain a light contact with your hand but push him forward strongly with your legs whenever he gets heavy, and bend him to the inside, then give with your inside hand when he lightens up. If 3, keep a strong contact with your legs and and a steady contact with your outside hand (it should feel like about a 3 pound weight in your hand) and give and receive with your inside hand as he lightens up, until you feel like you are controlling every stride.
OK, I only know English riding, but even a Western horse should progress through stages 1 and 2 in a snaffle bit. If your're riding Western and your horse wears a curb, I can't help you, but I also can't imagine a horse feeling "heavy" in that case. Hope this helps a little, and happy riding!

Thanx littledog987! That helps! I do ride english and the horse I'm riding is five. So he knows some things but not everything. Any other little tricks?

Also he is not being bad. He just naturaly is heavy.

My 5 year old western horse has never done that. I don't think.... Maybe the trainer worked on that.

Do most horses go through these stages?

I don't think so, but I may be wrong. Not every horse I've met has gone through these stages, only some.

I know pretty much nothing about training a horse for Western, except the beginning stages when they wear a snaffle bit, which seems about the same whether Western or English.

In my experience, all horses go through these stages, but some are faster than others. A horse who has really good conformation, superb natural balance and an excellent trainer may only need one or two lessons to get them beyond the need to lean on your hand. It also depends on the horse's and your personality, some horses consider leaning on your hand as a form of security. As an English rider (are you hunter, jumper, dressage or eventing? Please tell me, I'm curious) the horse moving forward is always the correct answer and deserves a reward.

You say your horse is 5, so he's probably past the stage of needing a direct rein that pulls him in the correct direction, and into the stage of security from leaning on your hand. What does your trainer say?? Push the horse forward, then take your trainer's advice about bending your horse with the inside hand or taking a strong hold with your outside hand.

this is a lot of great advice! i agree with a lot of it as well. lots of outside hand inside leg and half halt, half halt, half halt!as many walk trot transitions humaly (..horsily lol) possible. as soon as you feel your horse giving "release the spounge" in your inside hand. after a lot of work and a bit of fighting ( the horse will probaly try and canter on you) they should go on the bit and feel lighter in your hand.

So you know, I'm a hunter/jumper. Thank you that helps a lot. I have already started to use some of your suggestions and he is getting a little softer!!!!

Now that I think about it I agree with littledog987. All horses go through about all the same stages to find a way to get out of work. Sometimes the different stages last longer on different horses. Or sometimes (in my case) the horse may natural do some of these things.

Thanks Puppy-chow, for adding how important frequent half-halts are, for bringing your horse back to focusing on your attention in between releases. He probably will try to canter, but don't fight him for it, because the response of going forward is never the wrong answer--just go with it and take him back slowly and softly. Midnite, you're well on your way to training your horse to go happily and energetically but responsive to your most subtle cues.

ok it does depend on wether you are riding western or english. I ride english as I live there so I will give you tips that I have been given by top dressage riders. When the horse hangs on your hand one thing you can do is give one of your reins away. just slide it up the horses neck. This takes away the option of hanging on that rein. If u alternate the reins every time eventually he will get the message and slowly stop hanging on the reins.

Wow, I've never tried that but it makes a lot of sense. Keeping the same contact but just sliding your hand up the horse's neck would interrupt the leaning on your hand while not destroying the contact or the round frame you are working towards. Thanks, Sheeza!