The total weight of the arrow has nothing to do with the spine. There are carbon arrow that will spine correctly for your set up that weigh as little a 5. something grains per inch up to about 15 grains per inch.

A good weight arrow for a set up like yours would be somewhere around 450 grains to 500 grains. This will give you plenty of penetrating power while still allowing a fairly flat trajectory. An arrow of this weight will also keep your bow fairly quiet for hunting as well and will be much more pleasant to shoot.