I agree with Countrywood. IN ADDITION to all the riding suggestions. I have a large round pen, so it is not really lunging, but mine work in the round pen once a week or so. I use a Pessoa rig connected to a halter, not a bridle.
By cantering in the round pen, you can work on their strength and balance without all the distractions of a rider. You do not have to do a lot, and you certainly don’t have to crank him up. They have to be polite though, no running. Train them to do canter-trot transitions. A little goes a long way in the Pessoa rig even when very loose. On one of mine who wants to canter very low, I do set it up to mid- barrel after he is warmed up and this has helped lighten his canter.
He also does lots and lots of bounce poles and caveletti and lots of transitions while riding too. I find “heavy” to be sort of a relative term. If you pull back, they are heavy. It is really just obtaining a balance that you both like. I do recall that he had an atrocious canter as a youngster. For this particular horse, I did a lot of cantering where I found our balance, then sort of dropped him, then when he got too low, legged him into balance again, dropped him, repeat, repeat, until he held his balance and rhythm by himself for longer and longer. Can’t stand that “bumping” business, like the others said, you have to ride him up to your hands with your legs.