Balancing up on the right canter lead?

My horse is leaning into the turn on the right canter lead, so much that I have to find my outside seat and lean slightly outside to not feel like I am a motorcyclist, leaning around the next corner. I have tried giving him inside rein/leg to support his frame, but so far has not worked. This is particularly annoying when cantering a course. Anyone have a suggestion?

Instead of using more inside rein try using your outside rein to give him more support, try getting him round and bending on the turns as well and make sure he's not strung out, half halts might help too, I would practice with a lot of 20 meter circles and then see if it helps you on the course