How would you imagine your perfect Avatar-esque element fighting style?
All bending styles are based, at their core, on actual eastern martial arts and fighting techniques. For that reason, I believe the core of Gravity bending should be sumo. Sumo is based largely on an initial first charge and tackle, and then later by grabs meant to twist and turn, altering an opponent's momentum to toss them from the ring. Likewise, Gravity bending should be based on an initial charge, using your power to alter your mass for particularly powerful tackles. Then enhanced gravity can allow you to push your opponent down into the ground.
For balance reasons, I imagine gravity bending to be both rare and difficult to master, and so, like sumo, require diligence and strict adherence to practice that can sometimes be tainted by an excessive focus on tradition. Fledgling benders are encouraged to focus solely on their own momentum and density, as altering from further away becomes increasingly difficult and could lead to catastrophe.
Advanced techniques for the bending would be flight by nature of repelling yourself from the earth, slowing or stopping the opponent's movements at close range, launching projectiles of any sort, and creating shields of force that repel attacks. Movements at these ranges would resemble heavy movements and grabs in the air, or short, powerful slaps and chops.
Avatar and Master-level techniques include replication of water/earth/air and any other physical bending, imploding enemies, turning off enemy gravity to send them flying into space, or repelling any physical substance away from the body. Perfect control of gravity is an incredibly powerful force, with the potential to destroy or repel anything with amazing force. It is, at its strongest, both the perfect shield and the most deadly weapon.