So, if I'm understanding correctly, he accepts the pressure and responds, he's just really heavy on the bit.
It sounds like he's cheating and letting you support him with the reins instead of carrying himself. Little things to try are raising your hands slightly and using half halts while driving forward with your seat and legs to encourage him to lift up through his head and back and carry himself. Don't let him pull your upper body forward. The half halts are key because the pull and release doesn't give him anything to lean against.
My horse tends to get heavy on the bit too unless you really make her lighten up. For her, it's mostly a matter of getting her collected by driving her forward and using half halts. I also used to take her out into a large field with some hills and trot and canter up and down hills. This made a world of difference for her as it strengthened her back end and improved her impulsion. I'd warm her up out in the field on the hills and bring her into the ring and she'd be wonderfully light.