The correct joist depth depends on the thickness of the joist, the span, the material it's made of and the load placed on it. 8" is about average but it does depend on the other things.
Adding 2" timbers in the opposite direction will do little to upgrade your 6" timbers. You'd be better off adding 6" timbers in the same direction and somehow attaching them to the existing. But for a loft floor this really needs to be calculated and worked out properly.
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