Generally, you cannot have both.

I have found Goldtips and ST AXIS to be the strongest of the major brands, but neither are very light.

I've heard mixed reviews of the Carbon Tech Cheetahs & Carbon Revolution shafts.

CX arrows And Easton Litespeeds are a little more brittle than Goldtips/AXIS, but they are both pretty light and fairly strong. They need unibushings in the back though.